# NCERT solution class 12 chapter 2 Inverse Trigonometric Functions exercise 2.1 mathematics part 1

## EXERCISE 2.1

#### Question 1:

Find the principal value of

Let sin-1  Then sin y =

We know that the range of the principal value branch of sin−1 is

and sin

Therefore, the principal value of

#### Question 2:

Find the principal value of

We know that the range of the principal value branch of cos−1 is

.

Therefore, the principal value of.

#### Question 3:

Find the principal value of cosec−1 (2)

Let cosec−1 (2) = y. Then,

We know that the range of the principal value branch of cosec−1 is

Therefore, the principal value of

#### Question 4:

Find the principal value of

We know that the range of the principal value branch of tan−1 is

Therefore, the principal value of

#### Question 5:

Find the principal value of

We know that the range of the principal value branch of cos−1 is

Therefore, the principal value of

#### Question 6:

Find the principal value of tan−1 (−1)

Let tan−1 (−1) = y. Then,

We know that the range of the principal value branch of tan−1 is

Therefore, the principal value of

#### Question 7:

Find the principal value of

We know that the range of the principal value branch of sec−1 is

Therefore, the principal value of

#### Question 8:

Find the principal value of

We know that the range of the principal value branch of cot−1 is (0,π) and

Therefore, the principal value of

#### Question 9:

Find the principal value of

We know that the range of the principal value branch of cos−1 is [0,π] and

.

Therefore, the principal value of

#### Question 10:

Find the principal value of

We know that the range of the principal value branch of cosec−1 is

Therefore, the principal value of

#### Question 11:

Find the value of

#### Question 12:

Find the value of

#### Question 13:

Find the value of if sin−1 y, then

(A)  (B)

(C)  (D)

It is given that sin−1 y.

We know that the range of the principal value branch of sin−1 is

Therefore,.

#### Question 14:

Find the value of is equal to

(A) π (B)  (C)  (D)