**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

**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**: