## Exercise No. 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)