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Chapter 2 - Inverse Trigonometric FunctionsNCERT Solutions for Class 12 Science Math

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Exercise No. 2.1

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Question 1:

Find the principal value of
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Question 2:

Find the principal value of
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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)

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Question 4:

Find the principal value of
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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
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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)

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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
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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
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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
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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
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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
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Question 12:

Find the value of
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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
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