# NCERT solution class 12 chapter 2 Inverse Trigonometric Functions exercise 2.3 mathematics part 1

## EXERCISE 2.3

#### Question 1:

Find the value of

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

Here,

Now, can be written as:

#### Question 2:

Find the value 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:

Prove

Now, we have:

Prove

Now, we have:

#### Question 5:

Prove

Now, we will prove that:

Prove

Now, we have:

#### Question 7:

Prove

Using (1) and (2), we have

Prove

Prove

Prove

#### Question 11:

Prove  [Hint: putx = cos 2θ]

Prove

Solve

Solve

#### Question 15:

Solveis equal to

(A)  (B)  (C)  (D)

Let tan−1 x = y. Then,

#### Question 16:

Solvethen x is equal to

(A)  (B)  (C) 0 (D)

Therefore, from equation (1), we have

Put x = sin y. Then, we have:

But, when, it can be observed that:

is not the solution of the given equation.

Thus, x = 0.

Hence, the correct answer is C.

#### Question 17:

Solveis equal to

(A)  (B).  (C)  (D)