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need solution for RD Sharma maths class 12 chapter Inverse Trignometric Functions exercise 3.7 question 3 sub question (v)

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Answer: 1

Hint: The range of principal value of  \tan ^{-1} is \left [ -\frac{\pi }{2} ,\frac{\pi }{2}\right ]
Given:  \tan ^{-1}(\tan 1)

Explanation:

As we know \tan ^{-1}(\tan x)=x \text { if } x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]

By substituting this condition in given question

            \tan ^{-1}(\tan 1)=1

Hence, \tan ^{-1}(\tan 1)=1

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