# NCERT solution class 12 chapter 2 Inverse Trigonometric Functions exercise 2.2 mathematics part 1

## EXERCISE 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 8:

Write the function in the simplest form: tan-1cosx-sinxcosx+sinx=tan-11-sinxcosx1+sinxcosx=tan-11-tanx1+tanx=tan-11-tan-1tanx        tan-1x-y1+xy=tan-1x-tan-1y=π4-x

#### 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 19:

Find the values of is equal to

(A) (B) (C) (D) We know that cos−1 (cos x) = x if , which is the principal value branch of cos −1x.

Here, Now, can be written as:

cos-1cos7π6 = cos-1cosπ+π6cos-1cos7π6 = cos-1- cosπ6             as, cosπ+θ = – cos θcos-1cos7π6  = cos-1- cosπ-5π6cos-1cos7π6 = cos-1– cos 5π6   as, cosπ-θ = – cos θ #### 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   