Trigonometry Class 9th Mathematics Term 2 Tamilnadu Board Solution

Class 9^th Mathematics Term 2 Tamilnadu Board Solution

Exercise 2.1

1. From the following diagrams, find the trigonometric ratios of the angle θ…
2. From the following diagrams, find the trigonometric ratios of the angle θ…
3. From the following diagrams, find the trigonometric ratios of the angle θ…
4. From the following diagrams, find the trigonometric ratios of the angle θ…
5. From the following diagrams, find the trigonometric ratios of the angle θ…
6. From the following diagrams, find the trigonometric ratios of the angle θ…
7. From the following diagrams, find the trigonometric ratios of the angle θ…
8. From the following diagrams, find the trigonometric ratios of the angle θ…
9. sina = 9/15 Find the other trigonometric ratios of the following
10. sina = 9/15 Find the other trigonometric ratios of the following
11. cosa = 15/17 Find the other trigonometric ratios of the following…
12. cosa = 15/17 Find the other trigonometric ratios of the following…
13. tanp = 5/12 Find the other trigonometric ratios of the following
14. tanp = 5/12 Find the other trigonometric ratios of the following
15. sectheta = 17/8 Find the other trigonometric ratios of the following…
16. sectheta = 17/8 Find the other trigonometric ratios of the following…
17. cosectheta = 61/60 Find the other trigonometric ratios of the following…
18. cosectheta = 61/60 Find the other trigonometric ratios of the following…
19. sintegrate heta = x/y Find the other trigonometric ratios of the following…
20. sintegrate heta = x/y Find the other trigonometric ratios of the following…
21. (i) sintegrate heta = 1/root 2 (ii) sin θ = 0 (iii) tantheta = root 3 (iv)…
22. (i) sintegrate heta = 1/root 2 (ii) sin θ = 0 (iii) tantheta = root 3 (iv)…
23. In ΔABC, right angled at B, AB = 10 and AC = 26. Find the six trigonometric…
24. In ΔABC, right angled at B, AB = 10 and AC = 26. Find the six trigonometric…
25. If 5cos θ - 12 sin θ = 0, find sintegrate heta +costheta /2costheta -sintegrate…
26. If 5cos θ - 12 sin θ = 0, find sintegrate heta +costheta /2costheta -sintegrate…
27. If 29cosθ = 20 find sec^2 θ - tan^2 θ.
28. If 29cosθ = 20 find sec^2 θ - tan^2 θ.
29. If sectheta = 26/10 find 3costheta +4sintegrate heta /4costheta -2sintegrate…
30. If sectheta = 26/10 find 3costheta +4sintegrate heta /4costheta -2sintegrate…
31. If tantheta = a/b find sin^2 θ + cos^2 θ.
32. If tantheta = a/b find sin^2 θ + cos^2 θ.
33. If cottheta = 15/8 , evaluate (1+sintegrate heta) (1-sintegrate
34. If cottheta = 15/8 , evaluate (1+sintegrate heta) (1-sintegrate
35. In triangle PQR, right angled at Q, if tan p = 1/root 3 find the value of (i)…
36. In triangle PQR, right angled at Q, if tan p = 1/root 3 find the value of (i)…
37. If sectheta = 13/5 show that 2sintegrate heta -3costheta /4sintegrate heta…
38. If sectheta = 13/5 show that 2sintegrate heta -3costheta /4sintegrate heta…
39. If seca = 17/8 prove that 1-2 sin^2 A = 2cos^2 A - 1.
40. If seca = 17/8 prove that 1-2 sin^2 A = 2cos^2 A - 1.
41. (i) sin 45° + cos 45° (ii) sin 60° tan 30° (iii) tan45^circle /tan30^circle +…
42. (i) sin 45° + cos 45° (ii) sin 60° tan 30° (iii) tan45^circle /tan30^circle +…
43. (i) sin^2 30° + cos^2 30° = 1 (ii) 1 + tan^2 45° = sec^2 45° (iii) cos 60° = 1…
44. (i) sin^2 30° + cos^2 30° = 1 (ii) 1 + tan^2 45° = sec^2 45° (iii) cos 60° = 1…

Exercise 2.2

1. sin36^circle /cos54^circle Evaluate
2. sin36^circle /cos54^circle Evaluate
3. cosec10^circle /sec80^circle Evaluate
4. cosec10^circle /sec80^circle Evaluate
5. sin θ sec(90° - θ) Evaluate
6. sin θ sec(90° - θ) Evaluate
7. sec20^circle /cosec70^circle Evaluate
8. sec20^circle /cosec70^circle Evaluate
9. sin17^circle /cos73^circle Evaluate
10. sin17^circle /cos73^circle Evaluate
11. tan46^circle /cot44^circle Evaluate
12. tan46^circle /cot44^circle Evaluate
13. cos 38° cos 52° - sin 38° sin 52° Simplify
14. cos 38° cos 52° - sin 38° sin 52° Simplify
15. cos80^circle /sin10^circle + cos59^circle cosec31^circle Simplify…
16. cos80^circle /sin10^circle + cos59^circle cosec31^circle Simplify…
17. sin36^circle /cos54^circle - tan54^circle /cot36^circle Simplify
18. sin36^circle /cos54^circle - tan54^circle /cot36^circle Simplify
19. 3 tan67^circle /cot23^circle + 1/2 sin42^circle /cos48^circle + 5/2…
20. 3 tan67^circle /cot23^circle + 1/2 sin42^circle /cos48^circle + 5/2…
21. cos37^circle /sin53^circle x sin18^circle /cos72^circle Simplify
22. cos37^circle /sin53^circle x sin18^circle /cos72^circle Simplify
23. 2 sec (90^circle - theta)/cosectheta +7 cos (90^circle - theta)/sintegrate heta…
24. 2 sec (90^circle - theta)/cosectheta +7 cos (90^circle - theta)/sintegrate heta…
25. sec (90^circle - theta)/sin (90^circle - theta) x costheta /tan (90^circle -…
26. sec (90^circle - theta)/sin (90^circle - theta) x costheta /tan (90^circle -…
27. sin35^circle /cos55^circle + cos55^circle /sin35^circle - 2cos^260^circle…
28. sin35^circle /cos55^circle + cos55^circle /sin35^circle - 2cos^260^circle…
29. cot12° cot38° cot52° cot60° cot78°. Simplify
30. cot12° cot38° cot52° cot60° cot78°. Simplify
31. (i) sin A = cos 30° (ii) tan49° = cot A (iii) tan A tan 35° = 1 (iv) sec 35° =…
32. (i) sin A = cos 30° (ii) tan49° = cot A (iii) tan A tan 35° = 1 (iv) sec 35° =…
33. cos 48° - sin 42° = 0 Show that
34. cos 48° - sin 42° = 0 Show that
35. cos 20° cos 70° - sin 70° sin 20° = 0 Show that
36. cos 20° cos 70° - sin 70° sin 20° = 0 Show that
37. sin (90° - θ)tan θ = sin θ Show that
38. sin (90° - θ)tan θ = sin θ Show that
39. cos (90^circle - theta) tan (90^circle - theta)/costheta = 1 Show that…
40. cos (90^circle - theta) tan (90^circle - theta)/costheta = 1 Show that…

Exercise 2.3

1. sin 26o Find the value of the following.
2. sin 26o Find the value of the following.
3. cos 72o Find the value of the following.
4. cos 72o Find the value of the following.
5. tan35o Find the value of the following.
6. tan35o Find the value of the following.
7. sin 75o 15’ Find the value of the following.
8. sin 75o 15’ Find the value of the following.
9. sin 12° 12’ Find the value of the following.
10. sin 12° 12’ Find the value of the following.
11. cos 12o 35’ Find the value of the following.
12. cos 12o 35’ Find the value of the following.
13. cos 40o 20’ Find the value of the following.
14. cos 40o 20’ Find the value of the following.
15. tan 10o 26’ Find the value of the following.
16. tan 10o 26’ Find the value of the following.
17. cot 20o Find the value of the following.
18. cot 20o Find the value of the following.
19. cot 40^0 20’ Find the value of the following.
20. cot 40^0 20’ Find the value of the following.
21. (i) sinθ= 0.7009 (ii) cos θ = 0.9664 (iii) tan θ = 0.3679 (iv) cotθ = 0.2334 (v)…
22. (i) sinθ= 0.7009 (ii) cos θ = 0.9664 (iii) tan θ = 0.3679 (iv) cotθ = 0.2334 (v)…
23. sin 30°30’+cos 40°20’ Simplify, using trigonometric tables
24. sin 30°30’+cos 40°20’ Simplify, using trigonometric tables
25. tan 45° 27’ + sin 20° Simplify, using trigonometric tables
26. tan 45° 27’ + sin 20° Simplify, using trigonometric tables
27. tan 63°12’ - cos 12°42’ Simplify, using trigonometric tables
28. tan 63°12’ - cos 12°42’ Simplify, using trigonometric tables
29. sin 50° 26’ + cos 18° + tan 70° 12’ Simplify, using trigonometric tables…
30. sin 50° 26’ + cos 18° + tan 70° 12’ Simplify, using trigonometric tables…
31. tan 72° + cot 30° Simplify, using trigonometric tables
32. tan 72° + cot 30° Simplify, using trigonometric tables
33. Find the area of the right triangle with hypotenuse 20cm and one of the acute…
34. Find the area of the right triangle with hypotenuse 20cm and one of the acute…
35. Find the area of the triangle with hypotenuse 8cm and one of the acute angle is…
36. Find the area of the triangle with hypotenuse 8cm and one of the acute angle is…
37. Find the area of isosceles triangle with base 16cm and vertical angle 60° 40’…
38. Find the area of isosceles triangle with base 16cm and vertical angle 60° 40’…
39. Find the area of isosceles triangle with base 15cm and vertical angle 80°…
40. Find the area of isosceles triangle with base 15cm and vertical angle 80°…
41. A ladder makes an angle 30° with the floor and its lower end is 12m away from…
42. A ladder makes an angle 30° with the floor and its lower end is 12m away from…
43. Find the angle made by a ladder of length 4m with the ground if its one end is…
44. Find the angle made by a ladder of length 4m with the ground if its one end is…
45. Find the length of the chord of a circle of radius 5cm subtending an angle of…
46. Find the length of the chord of a circle of radius 5cm subtending an angle of…
47. Find the length of the side of regular polygon of 12 sides inscribed in a…
48. Find the length of the side of regular polygon of 12 sides inscribed in a…
49. Find the radius of the incircle of a regular hexagon of side 24cm.…
50. Find the radius of the incircle of a regular hexagon of side 24cm.…

Exercise 2.4

1. The value of sin^2 60° + cos^2 60° is equal toA. sin^2 45° + cos^2 45° B. tan^2…
2. The value of sin^2 60° + cos^2 60° is equal toA. sin^2 45° + cos^2 45° B. tan^2…
3. If x = 2tan30^circle /1-tan^230^circle , then the value of x isA. tan 45° B. tan…
4. If x = 2tan30^circle /1-tan^230^circle , then the value of x isA. tan 45° B. tan…
5. The value of sec^2 45° - tan^2 45° is equal toA. sin^2 60° - cos^2 60° B. sin^2…
6. The value of sec^2 45° - tan^2 45° is equal toA. sin^2 60° - cos^2 60° B. sin^2…
7. The value of 2sin30° cos30° is equal toA. tan 30° B. cos 60° C. sin 60° D. cot…
8. The value of 2sin30° cos30° is equal toA. tan 30° B. cos 60° C. sin 60° D. cot…
9. The value of cosec^2 60° - 1 is equal toA. cos^2 60° B. cot^2 60° C. sec^2 60°…
10. The value of cosec^2 60° - 1 is equal toA. cos^2 60° B. cot^2 60° C. sec^2 60°…
11. cos60° cos30° - sin60° sin30° is equal toA. cos 90° B. cosec 90° C. sin 30° +…
12. cos60° cos30° - sin60° sin30° is equal toA. cos 90° B. cosec 90° C. sin 30° +…
13. The value of sin27^0/cos63^circle isA.0 B. 1 C. tan 27° D. cot 63°…
14. The value of sin27^0/cos63^circle isA.0 B. 1 C. tan 27° D. cot 63°…
15. If cos x = sin 43°, then the value of x isA. 57° B. 43° C. 47° D. 90°…
16. If cos x = sin 43°, then the value of x isA. 57° B. 43° C. 47° D. 90°…
17. The value of sec 29° - cosec 61° isA. 1 B. 0 C. sec 60° D. cosec 29°…
18. The value of sec 29° - cosec 61° isA. 1 B. 0 C. sec 60° D. cosec 29°…
19. If 3x cosec 36° = sec 54°, then the value of x isA. 0 B. 1 C. 1/3 D. 3/4…
20. If 3x cosec 36° = sec 54°, then the value of x isA. 0 B. 1 C. 1/3 D. 3/4…
21. The value of sin60° cos30° + cos60° sin30° is equal toA. sec 90° B. tan 90° C.…
22. The value of sin60° cos30° + cos60° sin30° is equal toA. sec 90° B. tan 90° C.…
23. If cosacos30^circle = root 3/4 ,then the measure of A isA. 90° B. 60° C. 45° D.…
24. If cosacos30^circle = root 3/4 ,then the measure of A isA. 90° B. 60° C. 45° D.…
25. The value of tan26^circle /cot64^circle isA. 1/2 B. root 3/2 C. 0 D. 1…
26. The value of tan26^circle /cot64^circle isA. 1/2 B. root 3/2 C. 0 D. 1…
27. The value of sin 60° - cos 30° isA. 0 B. 1/root 2 C. root 3/2 D. 1…
28. The value of sin 60° - cos 30° isA. 0 B. 1/root 2 C. root 3/2 D. 1…
29. The value of cos^2 30° - sin^2 30° isA. cos 60° B. sin 60° C. 0 D. 1…
30. The value of cos^2 30° - sin^2 30° isA. cos 60° B. sin 60° C. 0 D. 1…

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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.

Find the other trigonometric ratios of the following

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.

Find the other trigonometric ratios of the following

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