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

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 

 and sin

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: