## EXERCISE 2.1

#### Page No 41:

#### Question 1:

Find the principal value of

#### Answer:

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

#### Answer:

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)

#### Answer:

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

#### Answer:

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

#### Answer:

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)

#### Answer:

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

#### Page No 42:

#### Question 7:

Find the principal value of

#### Answer:

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

#### Answer:

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

#### Answer:

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

#### Answer:

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

#### Answer:

#### Question 12:

Find the value of

#### Answer:

#### Question 13:

Find the value of if sin^{−1} *x *= *y*, then

**(****A)** **(B)**

**(****C)** **(D) **

#### Answer:

It is given that sin^{−1} *x *= *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) **

#### Answer: