Class 9th Mathematics Term 2 Tamilnadu Board Solution
Exercise 2.1- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- sina = 9/15 Find the other trigonometric ratios of the following
- sina = 9/15 Find the other trigonometric ratios of the following
- cosa = 15/17 Find the other trigonometric ratios of the following…
- cosa = 15/17 Find the other trigonometric ratios of the following…
- tanp = 5/12 Find the other trigonometric ratios of the following
- tanp = 5/12 Find the other trigonometric ratios of the following
- sectheta = 17/8 Find the other trigonometric ratios of the following…
- sectheta = 17/8 Find the other trigonometric ratios of the following…
- cosectheta = 61/60 Find the other trigonometric ratios of the following…
- cosectheta = 61/60 Find the other trigonometric ratios of the following…
- sintegrate heta = x/y Find the other trigonometric ratios of the following…
- sintegrate heta = x/y Find the other trigonometric ratios of the following…
- (i) sintegrate heta = 1/root 2 (ii) sin θ = 0 (iii) tantheta = root 3 (iv)…
- (i) sintegrate heta = 1/root 2 (ii) sin θ = 0 (iii) tantheta = root 3 (iv)…
- In ΔABC, right angled at B, AB = 10 and AC = 26. Find the six trigonometric…
- In ΔABC, right angled at B, AB = 10 and AC = 26. Find the six trigonometric…
- If 5cos θ - 12 sin θ = 0, find sintegrate heta +costheta /2costheta -sintegrate…
- If 5cos θ - 12 sin θ = 0, find sintegrate heta +costheta /2costheta -sintegrate…
- If 29cosθ = 20 find sec^2 θ - tan^2 θ.
- If 29cosθ = 20 find sec^2 θ - tan^2 θ.
- If sectheta = 26/10 find 3costheta +4sintegrate heta /4costheta -2sintegrate…
- If sectheta = 26/10 find 3costheta +4sintegrate heta /4costheta -2sintegrate…
- If tantheta = a/b find sin^2 θ + cos^2 θ.
- If tantheta = a/b find sin^2 θ + cos^2 θ.
- If cottheta = 15/8 , evaluate (1+sintegrate heta) (1-sintegrate
- If cottheta = 15/8 , evaluate (1+sintegrate heta) (1-sintegrate
- In triangle PQR, right angled at Q, if tan p = 1/root 3 find the value of (i)…
- In triangle PQR, right angled at Q, if tan p = 1/root 3 find the value of (i)…
- If sectheta = 13/5 show that 2sintegrate heta -3costheta /4sintegrate heta…
- If sectheta = 13/5 show that 2sintegrate heta -3costheta /4sintegrate heta…
- If seca = 17/8 prove that 1-2 sin^2 A = 2cos^2 A - 1.
- If seca = 17/8 prove that 1-2 sin^2 A = 2cos^2 A - 1.
- (i) sin 45° + cos 45° (ii) sin 60° tan 30° (iii) tan45^circle /tan30^circle +…
- (i) sin 45° + cos 45° (ii) sin 60° tan 30° (iii) tan45^circle /tan30^circle +…
- (i) sin^2 30° + cos^2 30° = 1 (ii) 1 + tan^2 45° = sec^2 45° (iii) cos 60° = 1…
- (i) sin^2 30° + cos^2 30° = 1 (ii) 1 + tan^2 45° = sec^2 45° (iii) cos 60° = 1…
Exercise 2.2- sin36^circle /cos54^circle Evaluate
- sin36^circle /cos54^circle Evaluate
- cosec10^circle /sec80^circle Evaluate
- cosec10^circle /sec80^circle Evaluate
- sin θ sec(90° - θ) Evaluate
- sin θ sec(90° - θ) Evaluate
- sec20^circle /cosec70^circle Evaluate
- sec20^circle /cosec70^circle Evaluate
- sin17^circle /cos73^circle Evaluate
- sin17^circle /cos73^circle Evaluate
- tan46^circle /cot44^circle Evaluate
- tan46^circle /cot44^circle Evaluate
- cos 38° cos 52° - sin 38° sin 52° Simplify
- cos 38° cos 52° - sin 38° sin 52° Simplify
- cos80^circle /sin10^circle + cos59^circle cosec31^circle Simplify…
- cos80^circle /sin10^circle + cos59^circle cosec31^circle Simplify…
- sin36^circle /cos54^circle - tan54^circle /cot36^circle Simplify
- sin36^circle /cos54^circle - tan54^circle /cot36^circle Simplify
- 3 tan67^circle /cot23^circle + 1/2 sin42^circle /cos48^circle + 5/2…
- 3 tan67^circle /cot23^circle + 1/2 sin42^circle /cos48^circle + 5/2…
- cos37^circle /sin53^circle x sin18^circle /cos72^circle Simplify
- cos37^circle /sin53^circle x sin18^circle /cos72^circle Simplify
- 2 sec (90^circle - theta)/cosectheta +7 cos (90^circle - theta)/sintegrate heta…
- 2 sec (90^circle - theta)/cosectheta +7 cos (90^circle - theta)/sintegrate heta…
- sec (90^circle - theta)/sin (90^circle - theta) x costheta /tan (90^circle -…
- sec (90^circle - theta)/sin (90^circle - theta) x costheta /tan (90^circle -…
- sin35^circle /cos55^circle + cos55^circle /sin35^circle - 2cos^260^circle…
- sin35^circle /cos55^circle + cos55^circle /sin35^circle - 2cos^260^circle…
- cot12° cot38° cot52° cot60° cot78°. Simplify
- cot12° cot38° cot52° cot60° cot78°. Simplify
- (i) sin A = cos 30° (ii) tan49° = cot A (iii) tan A tan 35° = 1 (iv) sec 35° =…
- (i) sin A = cos 30° (ii) tan49° = cot A (iii) tan A tan 35° = 1 (iv) sec 35° =…
- cos 48° - sin 42° = 0 Show that
- cos 48° - sin 42° = 0 Show that
- cos 20° cos 70° - sin 70° sin 20° = 0 Show that
- cos 20° cos 70° - sin 70° sin 20° = 0 Show that
- sin (90° - θ)tan θ = sin θ Show that
- sin (90° - θ)tan θ = sin θ Show that
- cos (90^circle - theta) tan (90^circle - theta)/costheta = 1 Show that…
- cos (90^circle - theta) tan (90^circle - theta)/costheta = 1 Show that…
Exercise 2.3- sin 26o Find the value of the following.
- sin 26o Find the value of the following.
- cos 72o Find the value of the following.
- cos 72o Find the value of the following.
- tan35o Find the value of the following.
- tan35o Find the value of the following.
- sin 75o 15’ Find the value of the following.
- sin 75o 15’ Find the value of the following.
- sin 12° 12’ Find the value of the following.
- sin 12° 12’ Find the value of the following.
- cos 12o 35’ Find the value of the following.
- cos 12o 35’ Find the value of the following.
- cos 40o 20’ Find the value of the following.
- cos 40o 20’ Find the value of the following.
- tan 10o 26’ Find the value of the following.
- tan 10o 26’ Find the value of the following.
- cot 20o Find the value of the following.
- cot 20o Find the value of the following.
- cot 40^0 20’ Find the value of the following.
- cot 40^0 20’ Find the value of the following.
- (i) sinθ= 0.7009 (ii) cos θ = 0.9664 (iii) tan θ = 0.3679 (iv) cotθ = 0.2334 (v)…
- (i) sinθ= 0.7009 (ii) cos θ = 0.9664 (iii) tan θ = 0.3679 (iv) cotθ = 0.2334 (v)…
- sin 30°30’+cos 40°20’ Simplify, using trigonometric tables
- sin 30°30’+cos 40°20’ Simplify, using trigonometric tables
- tan 45° 27’ + sin 20° Simplify, using trigonometric tables
- tan 45° 27’ + sin 20° Simplify, using trigonometric tables
- tan 63°12’ - cos 12°42’ Simplify, using trigonometric tables
- tan 63°12’ - cos 12°42’ Simplify, using trigonometric tables
- sin 50° 26’ + cos 18° + tan 70° 12’ Simplify, using trigonometric tables…
- sin 50° 26’ + cos 18° + tan 70° 12’ Simplify, using trigonometric tables…
- tan 72° + cot 30° Simplify, using trigonometric tables
- tan 72° + cot 30° Simplify, using trigonometric tables
- Find the area of the right triangle with hypotenuse 20cm and one of the acute…
- Find the area of the right triangle with hypotenuse 20cm and one of the acute…
- Find the area of the triangle with hypotenuse 8cm and one of the acute angle is…
- Find the area of the triangle with hypotenuse 8cm and one of the acute angle is…
- Find the area of isosceles triangle with base 16cm and vertical angle 60° 40’…
- Find the area of isosceles triangle with base 16cm and vertical angle 60° 40’…
- Find the area of isosceles triangle with base 15cm and vertical angle 80°…
- Find the area of isosceles triangle with base 15cm and vertical angle 80°…
- A ladder makes an angle 30° with the floor and its lower end is 12m away from…
- A ladder makes an angle 30° with the floor and its lower end is 12m away from…
- Find the angle made by a ladder of length 4m with the ground if its one end is…
- Find the angle made by a ladder of length 4m with the ground if its one end is…
- Find the length of the chord of a circle of radius 5cm subtending an angle of…
- Find the length of the chord of a circle of radius 5cm subtending an angle of…
- Find the length of the side of regular polygon of 12 sides inscribed in a…
- Find the length of the side of regular polygon of 12 sides inscribed in a…
- Find the radius of the incircle of a regular hexagon of side 24cm.…
- Find the radius of the incircle of a regular hexagon of side 24cm.…
Exercise 2.4- The value of sin^2 60° + cos^2 60° is equal toA. sin^2 45° + cos^2 45° B. tan^2…
- The value of sin^2 60° + cos^2 60° is equal toA. sin^2 45° + cos^2 45° B. tan^2…
- If x = 2tan30^circle /1-tan^230^circle , then the value of x isA. tan 45° B. tan…
- If x = 2tan30^circle /1-tan^230^circle , then the value of x isA. tan 45° B. tan…
- The value of sec^2 45° - tan^2 45° is equal toA. sin^2 60° - cos^2 60° B. sin^2…
- The value of sec^2 45° - tan^2 45° is equal toA. sin^2 60° - cos^2 60° B. sin^2…
- The value of 2sin30° cos30° is equal toA. tan 30° B. cos 60° C. sin 60° D. cot…
- The value of 2sin30° cos30° is equal toA. tan 30° B. cos 60° C. sin 60° D. cot…
- The value of cosec^2 60° - 1 is equal toA. cos^2 60° B. cot^2 60° C. sec^2 60°…
- The value of cosec^2 60° - 1 is equal toA. cos^2 60° B. cot^2 60° C. sec^2 60°…
- cos60° cos30° - sin60° sin30° is equal toA. cos 90° B. cosec 90° C. sin 30° +…
- cos60° cos30° - sin60° sin30° is equal toA. cos 90° B. cosec 90° C. sin 30° +…
- The value of sin27^0/cos63^circle isA.0 B. 1 C. tan 27° D. cot 63°…
- The value of sin27^0/cos63^circle isA.0 B. 1 C. tan 27° D. cot 63°…
- If cos x = sin 43°, then the value of x isA. 57° B. 43° C. 47° D. 90°…
- If cos x = sin 43°, then the value of x isA. 57° B. 43° C. 47° D. 90°…
- The value of sec 29° - cosec 61° isA. 1 B. 0 C. sec 60° D. cosec 29°…
- The value of sec 29° - cosec 61° isA. 1 B. 0 C. sec 60° D. cosec 29°…
- If 3x cosec 36° = sec 54°, then the value of x isA. 0 B. 1 C. 1/3 D. 3/4…
- If 3x cosec 36° = sec 54°, then the value of x isA. 0 B. 1 C. 1/3 D. 3/4…
- The value of sin60° cos30° + cos60° sin30° is equal toA. sec 90° B. tan 90° C.…
- The value of sin60° cos30° + cos60° sin30° is equal toA. sec 90° B. tan 90° C.…
- If cosacos30^circle = root 3/4 ,then the measure of A isA. 90° B. 60° C. 45° D.…
- If cosacos30^circle = root 3/4 ,then the measure of A isA. 90° B. 60° C. 45° D.…
- The value of tan26^circle /cot64^circle isA. 1/2 B. root 3/2 C. 0 D. 1…
- The value of tan26^circle /cot64^circle isA. 1/2 B. root 3/2 C. 0 D. 1…
- The value of sin 60° - cos 30° isA. 0 B. 1/root 2 C. root 3/2 D. 1…
- The value of sin 60° - cos 30° isA. 0 B. 1/root 2 C. root 3/2 D. 1…
- The value of cos^2 30° - sin^2 30° isA. cos 60° B. sin 60° C. 0 D. 1…
- The value of cos^2 30° - sin^2 30° isA. cos 60° B. sin 60° C. 0 D. 1…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- From the following diagrams, find the trigonometric ratios of the angle θ…
- sina = 9/15 Find the other trigonometric ratios of the following
- sina = 9/15 Find the other trigonometric ratios of the following
- cosa = 15/17 Find the other trigonometric ratios of the following…
- cosa = 15/17 Find the other trigonometric ratios of the following…
- tanp = 5/12 Find the other trigonometric ratios of the following
- tanp = 5/12 Find the other trigonometric ratios of the following
- sectheta = 17/8 Find the other trigonometric ratios of the following…
- sectheta = 17/8 Find the other trigonometric ratios of the following…
- cosectheta = 61/60 Find the other trigonometric ratios of the following…
- cosectheta = 61/60 Find the other trigonometric ratios of the following…
- sintegrate heta = x/y Find the other trigonometric ratios of the following…
- sintegrate heta = x/y Find the other trigonometric ratios of the following…
- (i) sintegrate heta = 1/root 2 (ii) sin θ = 0 (iii) tantheta = root 3 (iv)…
- (i) sintegrate heta = 1/root 2 (ii) sin θ = 0 (iii) tantheta = root 3 (iv)…
- In ΔABC, right angled at B, AB = 10 and AC = 26. Find the six trigonometric…
- In ΔABC, right angled at B, AB = 10 and AC = 26. Find the six trigonometric…
- If 5cos θ - 12 sin θ = 0, find sintegrate heta +costheta /2costheta -sintegrate…
- If 5cos θ - 12 sin θ = 0, find sintegrate heta +costheta /2costheta -sintegrate…
- If 29cosθ = 20 find sec^2 θ - tan^2 θ.
- If 29cosθ = 20 find sec^2 θ - tan^2 θ.
- If sectheta = 26/10 find 3costheta +4sintegrate heta /4costheta -2sintegrate…
- If sectheta = 26/10 find 3costheta +4sintegrate heta /4costheta -2sintegrate…
- If tantheta = a/b find sin^2 θ + cos^2 θ.
- If tantheta = a/b find sin^2 θ + cos^2 θ.
- If cottheta = 15/8 , evaluate (1+sintegrate heta) (1-sintegrate
- If cottheta = 15/8 , evaluate (1+sintegrate heta) (1-sintegrate
- In triangle PQR, right angled at Q, if tan p = 1/root 3 find the value of (i)…
- In triangle PQR, right angled at Q, if tan p = 1/root 3 find the value of (i)…
- If sectheta = 13/5 show that 2sintegrate heta -3costheta /4sintegrate heta…
- If sectheta = 13/5 show that 2sintegrate heta -3costheta /4sintegrate heta…
- If seca = 17/8 prove that 1-2 sin^2 A = 2cos^2 A - 1.
- If seca = 17/8 prove that 1-2 sin^2 A = 2cos^2 A - 1.
- (i) sin 45° + cos 45° (ii) sin 60° tan 30° (iii) tan45^circle /tan30^circle +…
- (i) sin 45° + cos 45° (ii) sin 60° tan 30° (iii) tan45^circle /tan30^circle +…
- (i) sin^2 30° + cos^2 30° = 1 (ii) 1 + tan^2 45° = sec^2 45° (iii) cos 60° = 1…
- (i) sin^2 30° + cos^2 30° = 1 (ii) 1 + tan^2 45° = sec^2 45° (iii) cos 60° = 1…
- sin36^circle /cos54^circle Evaluate
- sin36^circle /cos54^circle Evaluate
- cosec10^circle /sec80^circle Evaluate
- cosec10^circle /sec80^circle Evaluate
- sin θ sec(90° - θ) Evaluate
- sin θ sec(90° - θ) Evaluate
- sec20^circle /cosec70^circle Evaluate
- sec20^circle /cosec70^circle Evaluate
- sin17^circle /cos73^circle Evaluate
- sin17^circle /cos73^circle Evaluate
- tan46^circle /cot44^circle Evaluate
- tan46^circle /cot44^circle Evaluate
- cos 38° cos 52° - sin 38° sin 52° Simplify
- cos 38° cos 52° - sin 38° sin 52° Simplify
- cos80^circle /sin10^circle + cos59^circle cosec31^circle Simplify…
- cos80^circle /sin10^circle + cos59^circle cosec31^circle Simplify…
- sin36^circle /cos54^circle - tan54^circle /cot36^circle Simplify
- sin36^circle /cos54^circle - tan54^circle /cot36^circle Simplify
- 3 tan67^circle /cot23^circle + 1/2 sin42^circle /cos48^circle + 5/2…
- 3 tan67^circle /cot23^circle + 1/2 sin42^circle /cos48^circle + 5/2…
- cos37^circle /sin53^circle x sin18^circle /cos72^circle Simplify
- cos37^circle /sin53^circle x sin18^circle /cos72^circle Simplify
- 2 sec (90^circle - theta)/cosectheta +7 cos (90^circle - theta)/sintegrate heta…
- 2 sec (90^circle - theta)/cosectheta +7 cos (90^circle - theta)/sintegrate heta…
- sec (90^circle - theta)/sin (90^circle - theta) x costheta /tan (90^circle -…
- sec (90^circle - theta)/sin (90^circle - theta) x costheta /tan (90^circle -…
- sin35^circle /cos55^circle + cos55^circle /sin35^circle - 2cos^260^circle…
- sin35^circle /cos55^circle + cos55^circle /sin35^circle - 2cos^260^circle…
- cot12° cot38° cot52° cot60° cot78°. Simplify
- cot12° cot38° cot52° cot60° cot78°. Simplify
- (i) sin A = cos 30° (ii) tan49° = cot A (iii) tan A tan 35° = 1 (iv) sec 35° =…
- (i) sin A = cos 30° (ii) tan49° = cot A (iii) tan A tan 35° = 1 (iv) sec 35° =…
- cos 48° - sin 42° = 0 Show that
- cos 48° - sin 42° = 0 Show that
- cos 20° cos 70° - sin 70° sin 20° = 0 Show that
- cos 20° cos 70° - sin 70° sin 20° = 0 Show that
- sin (90° - θ)tan θ = sin θ Show that
- sin (90° - θ)tan θ = sin θ Show that
- cos (90^circle - theta) tan (90^circle - theta)/costheta = 1 Show that…
- cos (90^circle - theta) tan (90^circle - theta)/costheta = 1 Show that…
- sin 26o Find the value of the following.
- sin 26o Find the value of the following.
- cos 72o Find the value of the following.
- cos 72o Find the value of the following.
- tan35o Find the value of the following.
- tan35o Find the value of the following.
- sin 75o 15’ Find the value of the following.
- sin 75o 15’ Find the value of the following.
- sin 12° 12’ Find the value of the following.
- sin 12° 12’ Find the value of the following.
- cos 12o 35’ Find the value of the following.
- cos 12o 35’ Find the value of the following.
- cos 40o 20’ Find the value of the following.
- cos 40o 20’ Find the value of the following.
- tan 10o 26’ Find the value of the following.
- tan 10o 26’ Find the value of the following.
- cot 20o Find the value of the following.
- cot 20o Find the value of the following.
- cot 40^0 20’ Find the value of the following.
- cot 40^0 20’ Find the value of the following.
- (i) sinθ= 0.7009 (ii) cos θ = 0.9664 (iii) tan θ = 0.3679 (iv) cotθ = 0.2334 (v)…
- (i) sinθ= 0.7009 (ii) cos θ = 0.9664 (iii) tan θ = 0.3679 (iv) cotθ = 0.2334 (v)…
- sin 30°30’+cos 40°20’ Simplify, using trigonometric tables
- sin 30°30’+cos 40°20’ Simplify, using trigonometric tables
- tan 45° 27’ + sin 20° Simplify, using trigonometric tables
- tan 45° 27’ + sin 20° Simplify, using trigonometric tables
- tan 63°12’ - cos 12°42’ Simplify, using trigonometric tables
- tan 63°12’ - cos 12°42’ Simplify, using trigonometric tables
- sin 50° 26’ + cos 18° + tan 70° 12’ Simplify, using trigonometric tables…
- sin 50° 26’ + cos 18° + tan 70° 12’ Simplify, using trigonometric tables…
- tan 72° + cot 30° Simplify, using trigonometric tables
- tan 72° + cot 30° Simplify, using trigonometric tables
- Find the area of the right triangle with hypotenuse 20cm and one of the acute…
- Find the area of the right triangle with hypotenuse 20cm and one of the acute…
- Find the area of the triangle with hypotenuse 8cm and one of the acute angle is…
- Find the area of the triangle with hypotenuse 8cm and one of the acute angle is…
- Find the area of isosceles triangle with base 16cm and vertical angle 60° 40’…
- Find the area of isosceles triangle with base 16cm and vertical angle 60° 40’…
- Find the area of isosceles triangle with base 15cm and vertical angle 80°…
- Find the area of isosceles triangle with base 15cm and vertical angle 80°…
- A ladder makes an angle 30° with the floor and its lower end is 12m away from…
- A ladder makes an angle 30° with the floor and its lower end is 12m away from…
- Find the angle made by a ladder of length 4m with the ground if its one end is…
- Find the angle made by a ladder of length 4m with the ground if its one end is…
- Find the length of the chord of a circle of radius 5cm subtending an angle of…
- Find the length of the chord of a circle of radius 5cm subtending an angle of…
- Find the length of the side of regular polygon of 12 sides inscribed in a…
- Find the length of the side of regular polygon of 12 sides inscribed in a…
- Find the radius of the incircle of a regular hexagon of side 24cm.…
- Find the radius of the incircle of a regular hexagon of side 24cm.…
- The value of sin^2 60° + cos^2 60° is equal toA. sin^2 45° + cos^2 45° B. tan^2…
- The value of sin^2 60° + cos^2 60° is equal toA. sin^2 45° + cos^2 45° B. tan^2…
- If x = 2tan30^circle /1-tan^230^circle , then the value of x isA. tan 45° B. tan…
- If x = 2tan30^circle /1-tan^230^circle , then the value of x isA. tan 45° B. tan…
- The value of sec^2 45° - tan^2 45° is equal toA. sin^2 60° - cos^2 60° B. sin^2…
- The value of sec^2 45° - tan^2 45° is equal toA. sin^2 60° - cos^2 60° B. sin^2…
- The value of 2sin30° cos30° is equal toA. tan 30° B. cos 60° C. sin 60° D. cot…
- The value of 2sin30° cos30° is equal toA. tan 30° B. cos 60° C. sin 60° D. cot…
- The value of cosec^2 60° - 1 is equal toA. cos^2 60° B. cot^2 60° C. sec^2 60°…
- The value of cosec^2 60° - 1 is equal toA. cos^2 60° B. cot^2 60° C. sec^2 60°…
- cos60° cos30° - sin60° sin30° is equal toA. cos 90° B. cosec 90° C. sin 30° +…
- cos60° cos30° - sin60° sin30° is equal toA. cos 90° B. cosec 90° C. sin 30° +…
- The value of sin27^0/cos63^circle isA.0 B. 1 C. tan 27° D. cot 63°…
- The value of sin27^0/cos63^circle isA.0 B. 1 C. tan 27° D. cot 63°…
- If cos x = sin 43°, then the value of x isA. 57° B. 43° C. 47° D. 90°…
- If cos x = sin 43°, then the value of x isA. 57° B. 43° C. 47° D. 90°…
- The value of sec 29° - cosec 61° isA. 1 B. 0 C. sec 60° D. cosec 29°…
- The value of sec 29° - cosec 61° isA. 1 B. 0 C. sec 60° D. cosec 29°…
- If 3x cosec 36° = sec 54°, then the value of x isA. 0 B. 1 C. 1/3 D. 3/4…
- If 3x cosec 36° = sec 54°, then the value of x isA. 0 B. 1 C. 1/3 D. 3/4…
- The value of sin60° cos30° + cos60° sin30° is equal toA. sec 90° B. tan 90° C.…
- The value of sin60° cos30° + cos60° sin30° is equal toA. sec 90° B. tan 90° C.…
- If cosacos30^circle = root 3/4 ,then the measure of A isA. 90° B. 60° C. 45° D.…
- If cosacos30^circle = root 3/4 ,then the measure of A isA. 90° B. 60° C. 45° D.…
- The value of tan26^circle /cot64^circle isA. 1/2 B. root 3/2 C. 0 D. 1…
- The value of tan26^circle /cot64^circle isA. 1/2 B. root 3/2 C. 0 D. 1…
- The value of sin 60° - cos 30° isA. 0 B. 1/root 2 C. root 3/2 D. 1…
- The value of sin 60° - cos 30° isA. 0 B. 1/root 2 C. root 3/2 D. 1…
- The value of cos^2 30° - sin^2 30° isA. cos 60° B. sin 60° C. 0 D. 1…
- The value of cos^2 30° - sin^2 30° isA. cos 60° B. sin 60° C. 0 D. 1…
Exercise 2.1
Question 1.From the following diagrams, find the trigonometric ratios of the angle θ

Answer:
⇒ sin θ = 
cos θ = 
tan θ = 
cosec θ = 
sec θ = 
cot θ = 
Question 2.From the following diagrams, find the trigonometric ratios of the angle θ

Answer:
⇒ sin θ = 
cos θ = 
tan θ = 
cosec θ = 
sec θ = 
cot θ = 
Question 3.From the following diagrams, find the trigonometric ratios of the angle θ

Answer:
sin θ = 
cos θ = 
tan θ = 
cosec θ = 
sec θ = 
cot θ = 
Question 4.From the following diagrams, find the trigonometric ratios of the angle θ

Answer:
sin θ = 
cos θ = 
tan θ = 
cosec θ = 
sec θ = 
cot θ = 
Question 5.From the following diagrams, find the trigonometric ratios of the angle θ

Answer:
sin θ = 
cos θ = 
tan θ = 
cosec θ = 
sec θ = 
cot θ = 
Question 6.From the following diagrams, find the trigonometric ratios of the angle θ

Answer:
sin θ = 
cos θ = 
tan θ = 
cosec θ = 
sec θ = 
cot θ = 
Question 7.From the following diagrams, find the trigonometric ratios of the angle θ

Answer:
sin θ = 
cos θ = 
tan θ = 
cosec θ = 
sec θ = 
cot θ = 
Question 8.From the following diagrams, find the trigonometric ratios of the angle θ

Answer:
sin θ = 
cos θ = 
tan θ = 
cosec θ = 
sec θ = 
cot θ = 
Question 9.
Answer:

Let the third side be p,
By Pythagoras theorem,
⇒ 92 + p2 = 152
⇒ 81 + p2 = 225
⇒ p2 = 144
⇒ p = 12

Therefore, the other angles are:
cos A = 
tan A = 
cosec A = 
sec A = 
cot A = 
Question 10.
Answer:

Let the third side be p,
By Pythagoras theorem,
⇒ 92 + p2 = 152
⇒ 81 + p2 = 225
⇒ p2 = 144
⇒ p = 12

Therefore, the other angles are:
cos A = 
tan A = 
cosec A = 
sec A = 
cot A = 
Question 11.Find the other trigonometric ratios of the following

Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 152 + p2 = 172
⇒ 225 + p2 = 289
⇒ p2 = 64
⇒ p = 8

Therefore, the other angles are:
sin P = 
tan P = 
cosec P = 
sec P = 
cot P = 
Question 12.Find the other trigonometric ratios of the following

Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 152 + p2 = 172
⇒ 225 + p2 = 289
⇒ p2 = 64
⇒ p = 8

Therefore, the other angles are:
sin P = 
tan P = 
cosec P = 
sec P = 
cot P = 
Question 13.Find the other trigonometric ratios of the following

Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 52 + 122 = P2
⇒ 25 + 144 = p2
⇒ p2 = 169
⇒ p = 13

Therefore, the other angles are:
sin P = 
cos P = 
cosec P = 
sec P = 
cot P = 
Question 14.Find the other trigonometric ratios of the following

Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 52 + 122 = P2
⇒ 25 + 144 = p2
⇒ p2 = 169
⇒ p = 13

Therefore, the other angles are:
sin P = 
cos P = 
cosec P = 
sec P = 
cot P = 
Question 15.Find the other trigonometric ratios of the following

Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 152 + p2 = 172
⇒ 64 + p2 = 289
⇒ p2 = 225
⇒ p = 15

Therefore, the other angles are:
sin θ = 
cos θ = 
tan θ = 
cosec θ = 
cot θ = 
Question 16.Find the other trigonometric ratios of the following

Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 152 + p2 = 172
⇒ 64 + p2 = 289
⇒ p2 = 225
⇒ p = 15

Therefore, the other angles are:
sin θ = 
cos θ = 
tan θ = 
cosec θ = 
cot θ = 
Question 17.Find the other trigonometric ratios of the following

Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 602 + p2 = 612
⇒ 3600 + p2 = 3721
⇒ p2 = 121
⇒ p = 11

Therefore, the other angles are:
sin θ = 
cos θ = 
tan θ = 
sec θ = 
cot θ = 
Question 18.Find the other trigonometric ratios of the following

Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 602 + p2 = 612
⇒ 3600 + p2 = 3721
⇒ p2 = 121
⇒ p = 11

Therefore, the other angles are:
sin θ = 
cos θ = 
tan θ = 
sec θ = 
cot θ = 
Question 19.Find the other trigonometric ratios of the following

Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ x2 + p2 = y2
⇒ p2 = y2 – x2
⇒ p = √y2 – x2

Therefore, the other angles are:
cos θ = 
tan θ = 
cosec θ = 
sec θ = 
cot θ = 
Question 20.Find the other trigonometric ratios of the following

Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ x2 + p2 = y2
⇒ p2 = y2 – x2
⇒ p = √y2 – x2

Therefore, the other angles are:
cos θ = 
tan θ = 
cosec θ = 
sec θ = 
cot θ = 
Question 21.Find the value of θ, if
(i) 
(ii) sin θ = 0
(iii) 
(iv) 
Answer:
(i) 
θ = 45° (From the table)
(ii) 
θ = 0° (From the table)
(iii) 
θ = 60° (From the table)
(iv) 
θ = 30° (From the table)
Question 22.Find the value of θ, if
(i) 
(ii) sin θ = 0
(iii) 
(iv) 
Answer:
(i) 
sin θ = sin 45°
θ = 45° (From the table)
(ii) 
sin θ = sin 0°
θ = 0° (From the table)
(iii) 
tan θ = tan 60°
θ = 60° (From the table)
(iv) 
cos θ = cos 30°
θ = 30° (From the table)
Question 23.In ΔABC, right angled at B, AB = 10 and AC = 26. Find the six trigonometric ratios of the angles A and C.
Answer:

For ∠A:
sin A = 
cos A = 
tan A = 
cosec A = 
sec A = 
cot A = 
For ∠C:
sin C = 
cos C = 
tan C = 
cosec C = 
sec C = 
cot C = 
Question 24.In ΔABC, right angled at B, AB = 10 and AC = 26. Find the six trigonometric ratios of the angles A and C.
Answer:

For ∠A:
sin A = 
cos A = 
tan A = 
cosec A = 
sec A = 
cot A = 
For ∠C:
sin C = 
cos C = 
tan C = 
cosec C = 
sec C = 
cot C = 
Question 25.If 5cos θ – 12 sin θ = 0, find 
Answer:5cosθ –12sinθ = 0
⇒ 5cosθ = 12sinθ
⇒ tanθ = 5/12

Let the third side be p,
By Pythagoras theorem,
⇒ 52 + 122 = P2
⇒ 25 + 144 = p2
⇒ p2 = 169
⇒ p = 13

Therefore, the other angles are:
sin θ = 
cos θ = 
Putting values in the function as:
⇒ 
⇒ 
⇒ 
Question 26.If 5cos θ – 12 sin θ = 0, find 
Answer:5cosθ –12sinθ = 0
⇒ 5cosθ = 12sinθ
⇒ tanθ = 5/12

Let the third side be p,
By Pythagoras theorem,
⇒ 52 + 122 = P2
⇒ 25 + 144 = p2
⇒ p2 = 169
⇒ p = 13

Therefore, the other angles are:
sin θ = 
cos θ = 
Putting values in the function as:
⇒ 
⇒ 
⇒ 
Question 27.If 29cosθ = 20 find sec2 θ – tan2 θ.
Answer:
29cosθ = 20
⇒ cosθ = 20/29

Let the third side be p,
By Pythagoras theorem,
⇒ 202 + p2 = 292
⇒ 400 + p2 = 841
⇒ p2 = 441
⇒ p = 21

Therefore, the other angles are:
sec θ = 
tan θ = 
Putting the values in function:
⇒ sec2 θ – tan2 θ
⇒ 
⇒ 
⇒ 
Question 28.If 29cosθ = 20 find sec2 θ – tan2 θ.
Answer:
29cosθ = 20
⇒ cosθ = 20/29

Let the third side be p,
By Pythagoras theorem,
⇒ 202 + p2 = 292
⇒ 400 + p2 = 841
⇒ p2 = 441
⇒ p = 21

Therefore, the other angles are:
sec θ = 
tan θ = 
Putting the values in function:
⇒ sec2 θ – tan2 θ
⇒ 
⇒ 
⇒ 
Question 29.If
find
.
Answer:

∠BAC = θ
Let the third side be p,
By Pythagoras theorem,
⇒ 102 + p2 = 262
⇒ 100 + p2 = 676
⇒ p2 = 576
⇒ p = 24

Therefore, the other angles are:
sin θ = 
cos θ = 
Putting values in the function as:
⇒ 
⇒ 
⇒ 
Question 30.If
find
.
Answer:

∠BAC = θ
Let the third side be p,
By Pythagoras theorem,
⇒ 102 + p2 = 262
⇒ 100 + p2 = 676
⇒ p2 = 576
⇒ p = 24

Therefore, the other angles are:
sin θ = 
cos θ = 
Putting values in the function as:
⇒ 
⇒ 
⇒ 
Question 31.If
find sin2 θ + cos2 θ.
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ a2 + b2 = p2
⇒ p = √a2 + b2

Therefore, the other angles are:
sin θ = 
cos θ = 
Putting the values in function:
⇒ sin2 θ + cos2 θ
⇒ 
⇒ 
⇒ 
Question 32.If
find sin2 θ + cos2 θ.
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ a2 + b2 = p2
⇒ p = √a2 + b2

Therefore, the other angles are:
sin θ = 
cos θ = 
Putting the values in function:
⇒ sin2 θ + cos2 θ
⇒ 
⇒ 
⇒ 
Question 33.If
, evaluate
Answer:Simplifying the function:
⇒ 
⇒ 

Let the third side be p,
By Pythagoras theorem,
⇒ 82 + 152 = P2
⇒ 64 + 225 = p2
⇒ p2 = 289
⇒ p = 17

Therefore, the other angles are:
sin θ = 
cos θ = 
Putting these values in the simplied function:
⇒ 
⇒ 
⇒ 
⇒ 
Question 34.If
, evaluate
Answer:Simplifying the function:
⇒ 
⇒ 

Let the third side be p,
By Pythagoras theorem,
⇒ 82 + 152 = P2
⇒ 64 + 225 = p2
⇒ p2 = 289
⇒ p = 17

Therefore, the other angles are:
sin θ = 
cos θ = 
Putting these values in the simplied function:
⇒ 
⇒ 
⇒ 
⇒ 
Question 35.In triangle PQR, right angled at Q, if tan
find the value of
(i) sin P cos R + cos P sin R
(ii) cos P cos R – sin P sin R.
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 12 + (√3)2 = P2
⇒ 1 + 3 = p2
⇒ p2 = 4
⇒ p = 2

Therefore, the other angles are:
sin P = 
cos P = 
sin R = 
cos R = 
(i) Putting the values in the expression:
sin P cos R + cos P sin R
⇒ 
⇒ 
⇒ 1
(ii) Putting the values in the expression:
cos P cos R – sin P sin R.
⇒ 
⇒ 0
Question 36.In triangle PQR, right angled at Q, if tan
find the value of
(i) sin P cos R + cos P sin R
(ii) cos P cos R – sin P sin R.
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 12 + (√3)2 = P2
⇒ 1 + 3 = p2
⇒ p2 = 4
⇒ p = 2

Therefore, the other angles are:
sin P = 
cos P = 
sin R = 
cos R = 
(i) Putting the values in the expression:
sin P cos R + cos P sin R
⇒ 
⇒ 
⇒ 1
(ii) Putting the values in the expression:
cos P cos R – sin P sin R.
⇒ 
⇒ 0
Question 37.If
show that 
Answer:

Let the third side be p,
By Pythagoras theorem,
⇒ 52 + p2 = 132
⇒ 25 + p2 = 169
⇒ p2 = 144
⇒ p = 12

Therefore, the other angles are:
sin θ = 
cos θ = 
Putting these values in the left hand side:
⇒ 
⇒ 
⇒ 
⇒ 3
Which is equal to right hand side.
Hence proved.
Question 38.If
show that 
Answer:

Let the third side be p,
By Pythagoras theorem,
⇒ 52 + p2 = 132
⇒ 25 + p2 = 169
⇒ p2 = 144
⇒ p = 12

Therefore, the other angles are:
sin θ = 
cos θ = 
Putting these values in the left hand side:
⇒ 
⇒ 
⇒ 
⇒ 3
Which is equal to right hand side.
Hence proved.
Question 39.If
prove that 1–2 sin2A = 2cos2A – 1.
Answer:


Let the third side be p,
By Pythagoras theorem,
⇒ 82 + p2 = 172
⇒ 64 + p2 = 289
⇒ p2 = 225
⇒ p = 15
Therefore, the other angles are:
sin θ = 
cos θ = 
Putting these values in the left hand side:
⇒ 1–2×
⇒ 1–2×
⇒ 1–
⇒ 
Putting values in the right hand side:
⇒ 2×
⇒ 2×
–1
⇒ 
⇒ 
Therefore, Left hand side and right hand side are equal.
Hence proved.
Question 40.If 
From the following diagrams, find the trigonometric ratios of the angle θ
Answer:
⇒ sin θ =
cos θ =
tan θ =
cosec θ =
sec θ =
cot θ =
Question 2.
From the following diagrams, find the trigonometric ratios of the angle θ
Answer:
⇒ sin θ =
cos θ =
tan θ =
cosec θ =
sec θ =
cot θ =
Question 3.
From the following diagrams, find the trigonometric ratios of the angle θ
Answer:
sin θ =
cos θ =
tan θ =
cosec θ =
sec θ =
cot θ =
Question 4.
From the following diagrams, find the trigonometric ratios of the angle θ
Answer:
sin θ =
cos θ =
tan θ =
cosec θ =
sec θ =
cot θ =
Question 5.
From the following diagrams, find the trigonometric ratios of the angle θ
Answer:
sin θ =
cos θ =
tan θ =
cosec θ =
sec θ =
cot θ =
Question 6.
From the following diagrams, find the trigonometric ratios of the angle θ
Answer:
sin θ =
cos θ =
tan θ =
cosec θ =
sec θ =
cot θ =
Question 7.
From the following diagrams, find the trigonometric ratios of the angle θ
Answer:
sin θ =
cos θ =
tan θ =
cosec θ =
sec θ =
cot θ =
Question 8.
From the following diagrams, find the trigonometric ratios of the angle θ
Answer:
sin θ =
cos θ =
tan θ =
cosec θ =
sec θ =
cot θ =
Question 9.
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 92 + p2 = 152
⇒ 81 + p2 = 225
⇒ p2 = 144
⇒ p = 12
Therefore, the other angles are:
cos A =
tan A =
cosec A =
sec A =
cot A =
Question 10.
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 92 + p2 = 152
⇒ 81 + p2 = 225
⇒ p2 = 144
⇒ p = 12
Therefore, the other angles are:
cos A =
tan A =
cosec A =
sec A =
cot A =
Question 11.
Find the other trigonometric ratios of the following
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 152 + p2 = 172
⇒ 225 + p2 = 289
⇒ p2 = 64
⇒ p = 8
Therefore, the other angles are:
sin P =
tan P =
cosec P =
sec P =
cot P =
Question 12.
Find the other trigonometric ratios of the following
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 152 + p2 = 172
⇒ 225 + p2 = 289
⇒ p2 = 64
⇒ p = 8
Therefore, the other angles are:
sin P =
tan P =
cosec P =
sec P =
cot P =
Question 13.
Find the other trigonometric ratios of the following
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 52 + 122 = P2
⇒ 25 + 144 = p2
⇒ p2 = 169
⇒ p = 13
Therefore, the other angles are:
sin P =
cos P =
cosec P =
sec P =
cot P =
Question 14.
Find the other trigonometric ratios of the following
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 52 + 122 = P2
⇒ 25 + 144 = p2
⇒ p2 = 169
⇒ p = 13
Therefore, the other angles are:
sin P =
cos P =
cosec P =
sec P =
cot P =
Question 15.
Find the other trigonometric ratios of the following
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 152 + p2 = 172
⇒ 64 + p2 = 289
⇒ p2 = 225
⇒ p = 15
Therefore, the other angles are:
sin θ =
cos θ =
tan θ =
cosec θ =
cot θ =
Question 16.
Find the other trigonometric ratios of the following
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 152 + p2 = 172
⇒ 64 + p2 = 289
⇒ p2 = 225
⇒ p = 15
Therefore, the other angles are:
sin θ =
cos θ =
tan θ =
cosec θ =
cot θ =
Question 17.
Find the other trigonometric ratios of the following
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 602 + p2 = 612
⇒ 3600 + p2 = 3721
⇒ p2 = 121
⇒ p = 11
Therefore, the other angles are:
sin θ =
cos θ =
tan θ =
sec θ =
cot θ =
Question 18.
Find the other trigonometric ratios of the following
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 602 + p2 = 612
⇒ 3600 + p2 = 3721
⇒ p2 = 121
⇒ p = 11
Therefore, the other angles are:
sin θ =
cos θ =
tan θ =
sec θ =
cot θ =
Question 19.
Find the other trigonometric ratios of the following
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ x2 + p2 = y2
⇒ p2 = y2 – x2
⇒ p = √y2 – x2
Therefore, the other angles are:
cos θ =
tan θ =
cosec θ =
sec θ =
cot θ =
Question 20.
Find the other trigonometric ratios of the following
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ x2 + p2 = y2
⇒ p2 = y2 – x2
⇒ p = √y2 – x2
Therefore, the other angles are:
cos θ =
tan θ =
cosec θ =
sec θ =
cot θ =
Question 21.
Find the value of θ, if
(i)
(ii) sin θ = 0
(iii)
(iv)
Answer:
(i)
θ = 45° (From the table)
(ii)
θ = 0° (From the table)
(iii)
θ = 60° (From the table)
(iv)
θ = 30° (From the table)
Question 22.
Find the value of θ, if
(i)
(ii) sin θ = 0
(iii)
(iv)
Answer:
(i)
θ = 45° (From the table)
(ii)
θ = 0° (From the table)
(iii)
θ = 60° (From the table)
(iv)
cos θ = cos 30°
θ = 30° (From the table)
Question 23.
In ΔABC, right angled at B, AB = 10 and AC = 26. Find the six trigonometric ratios of the angles A and C.
Answer:
For ∠A:
sin A =
cos A =
tan A =
cosec A =
sec A =
cot A =
For ∠C:
sin C =
cos C =
tan C =
cosec C =
sec C =
cot C =
Question 24.
In ΔABC, right angled at B, AB = 10 and AC = 26. Find the six trigonometric ratios of the angles A and C.
Answer:
For ∠A:
sin A =
cos A =
tan A =
cosec A =
sec A =
cot A =
For ∠C:
sin C =
cos C =
tan C =
cosec C =
sec C =
cot C =
Question 25.
If 5cos θ – 12 sin θ = 0, find
Answer:
5cosθ –12sinθ = 0
⇒ 5cosθ = 12sinθ
⇒ tanθ = 5/12
Let the third side be p,
By Pythagoras theorem,
⇒ 52 + 122 = P2
⇒ 25 + 144 = p2
⇒ p2 = 169
⇒ p = 13
Therefore, the other angles are:
sin θ =
cos θ =
Putting values in the function as:
⇒
⇒
⇒
Question 26.
If 5cos θ – 12 sin θ = 0, find
Answer:
5cosθ –12sinθ = 0
⇒ 5cosθ = 12sinθ
⇒ tanθ = 5/12
Let the third side be p,
By Pythagoras theorem,
⇒ 52 + 122 = P2
⇒ 25 + 144 = p2
⇒ p2 = 169
⇒ p = 13
Therefore, the other angles are:
sin θ =
cos θ =
Putting values in the function as:
⇒
⇒
⇒
Question 27.
If 29cosθ = 20 find sec2 θ – tan2 θ.
Answer:
29cosθ = 20
⇒ cosθ = 20/29
Let the third side be p,
By Pythagoras theorem,
⇒ 202 + p2 = 292
⇒ 400 + p2 = 841
⇒ p2 = 441
⇒ p = 21
Therefore, the other angles are:
sec θ =
tan θ =
Putting the values in function:
⇒ sec2 θ – tan2 θ
⇒
⇒
⇒
Question 28.
If 29cosθ = 20 find sec2 θ – tan2 θ.
Answer:
29cosθ = 20
⇒ cosθ = 20/29
Let the third side be p,
By Pythagoras theorem,
⇒ 202 + p2 = 292
⇒ 400 + p2 = 841
⇒ p2 = 441
⇒ p = 21
Therefore, the other angles are:
sec θ =
tan θ =
Putting the values in function:
⇒ sec2 θ – tan2 θ
⇒
⇒
⇒
Question 29.
If find
.
Answer:
∠BAC = θ
Let the third side be p,
By Pythagoras theorem,
⇒ 102 + p2 = 262
⇒ 100 + p2 = 676
⇒ p2 = 576
⇒ p = 24
Therefore, the other angles are:
sin θ =
cos θ =
Putting values in the function as:
⇒
⇒
⇒
Question 30.
If find
.
Answer:
∠BAC = θ
Let the third side be p,
By Pythagoras theorem,
⇒ 102 + p2 = 262
⇒ 100 + p2 = 676
⇒ p2 = 576
⇒ p = 24
Therefore, the other angles are:
sin θ =
cos θ =
Putting values in the function as:
⇒
⇒
⇒
Question 31.
If find sin2 θ + cos2 θ.
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ a2 + b2 = p2
⇒ p = √a2 + b2
Therefore, the other angles are:
sin θ =
cos θ =
Putting the values in function:
⇒ sin2 θ + cos2 θ
⇒
⇒
⇒
Question 32.
If find sin2 θ + cos2 θ.
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ a2 + b2 = p2
⇒ p = √a2 + b2
Therefore, the other angles are:
sin θ =
cos θ =
Putting the values in function:
⇒ sin2 θ + cos2 θ
⇒
⇒
⇒
Question 33.
If , evaluate
Answer:
Simplifying the function:
⇒
⇒
Let the third side be p,
By Pythagoras theorem,
⇒ 82 + 152 = P2
⇒ 64 + 225 = p2
⇒ p2 = 289
⇒ p = 17
Therefore, the other angles are:
sin θ =
cos θ =
Putting these values in the simplied function:
⇒
⇒
⇒
⇒
Question 34.
If , evaluate
Answer:
Simplifying the function:
⇒
⇒
Let the third side be p,
By Pythagoras theorem,
⇒ 82 + 152 = P2
⇒ 64 + 225 = p2
⇒ p2 = 289
⇒ p = 17
Therefore, the other angles are:
sin θ =
cos θ =
Putting these values in the simplied function:
⇒
⇒
⇒
⇒
Question 35.
In triangle PQR, right angled at Q, if tan find the value of
(i) sin P cos R + cos P sin R
(ii) cos P cos R – sin P sin R.
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 12 + (√3)2 = P2
⇒ 1 + 3 = p2
⇒ p2 = 4
⇒ p = 2
Therefore, the other angles are:
sin P =
cos P =
sin R =
cos R =
(i) Putting the values in the expression:
sin P cos R + cos P sin R
⇒
⇒
⇒ 1
(ii) Putting the values in the expression:
cos P cos R – sin P sin R.
⇒
⇒ 0
Question 36.
In triangle PQR, right angled at Q, if tan find the value of
(i) sin P cos R + cos P sin R
(ii) cos P cos R – sin P sin R.
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 12 + (√3)2 = P2
⇒ 1 + 3 = p2
⇒ p2 = 4
⇒ p = 2
Therefore, the other angles are:
sin P =
cos P =
sin R =
cos R =
(i) Putting the values in the expression:
sin P cos R + cos P sin R
⇒
⇒
⇒ 1
(ii) Putting the values in the expression:
cos P cos R – sin P sin R.
⇒
⇒ 0
Question 37.
If show that
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 52 + p2 = 132
⇒ 25 + p2 = 169
⇒ p2 = 144
⇒ p = 12
Therefore, the other angles are:
sin θ =
cos θ =
Putting these values in the left hand side:
⇒
⇒
⇒
⇒ 3
Which is equal to right hand side.
Hence proved.
Question 38.
If show that
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 52 + p2 = 132
⇒ 25 + p2 = 169
⇒ p2 = 144
⇒ p = 12
Therefore, the other angles are:
sin θ =
cos θ =
Putting these values in the left hand side:
⇒
⇒
⇒
⇒ 3
Which is equal to right hand side.
Hence proved.
Question 39.
If prove that 1–2 sin2A = 2cos2A – 1.
Answer:
Let the third side be p,
By Pythagoras theorem,
⇒ 82 + p2 = 172
⇒ 64 + p2 = 289
⇒ p2 = 225
⇒ p = 15
Therefore, the other angles are:
sin θ =
cos θ =
Putting these values in the left hand side:
⇒ 1–2×
⇒ 1–2×
⇒ 1–
⇒
Putting values in the right hand side:
⇒ 2×
⇒ 2× –1
⇒
⇒
Therefore, Left hand side and right hand side are equal.
Hence proved.
Question 40.
If