# Exercise No. 2.2

#### Question 1:

Prove To prove: Let x = sinθ. Then, We have,
R.H.S. =  = 3θ = L.H.S.

#### Question 2:

Prove To prove: Let x = cosθ. Then, cos−1 x =θ.
We have, #### Question 3:

Prove To prove:  #### Question 4:

Prove To prove:  #### Question 5:

Write the function in the simplest form:  #### Question 6:

Write the function in the simplest form:  Put x = cosec θ ⇒ θ = cosec−1 x #### Question 7:

Write the function in the simplest form:  #### Question 9:

Write the function in the simplest form:  #### Question 10:

Write the function in the simplest form:  #### Question 11:

Find the value of Let . Then,  #### Question 12:

Find the value of  #### Question 13:

Find the value of Let x = tan θ. Then, θ = tan−1 x. Let y = tan Φ. Then, Φ = tan−1 y. #### Question 14:

If , then find the value of x. On squaring both sides, we get:  Hence, the value of x is #### Question 15:

If , then find the value of x. Hence, the value of x is #### Question 16:

Find the values of  We know that sin−1 (sin x) = x if , which is the principal value branch of sin−1x.
Here, Now, can be written as:  #### Question 17:

Find the values of  We know that tan−1 (tan x) = x if , which is the principal value branch of tan−1x.
Here, Now, can be written as:  #### Question 18:

Find the values of Let . Then,  #### Question 20:

Find the values of is equal to
(A) (B) (C) (D)1

Let . Then, We know that the range of the principal value branch of .  #### Question 21:

Find the values of is equal to
(A)π (B) (C) 0 (D) Let . Then, We know that the range of the principal value branch of  Let . The range of the principal value branch of  