## 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) 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)  