Chapter 2 - Inverse Trigonometric FunctionsNCERT Solutions for Class 12 Science Math
Exercise No. 2.1
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


Therefore, the principal value of 

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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
.

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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 

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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 

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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 

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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 

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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 

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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 

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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 

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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 

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Question 11:
Find the value of 

ANSWER:

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Question 12:
Find the value of 

ANSWER:

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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,
.

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Question 14:
Find the value of
is equal to

(A)π(B)
(C)
(D) 



ANSWER:
