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  • Need solution for RD Sharma maths class 12 chapter 3 Inverse Trigonometric Functions exercise  Very short answer question 27 math

Need solution for RD Sharma maths class 12 chapter 3 Inverse Trigonometric Functions exercise  Very short answer question 27 math

Answers (1)

Answer:-\frac{\pi}{4}

Given: \tan ^{-1}\left\{\tan \left(\frac{15 \pi}{4}\right)\right\}

Hint: Try to solve the \tan  function first.

\therefore \tan (4 \pi-x)=-\tan x

Solution:      

\begin{aligned} \tan ^{-1}\left\{\tan \left(\frac{15 \pi}{4}\right)\right\} &=\tan ^{-1}\left\{\tan \left(4 \pi-\frac{\pi}{4}\right)\right\} \\ &=\tan ^{-1}\left\{\tan \left(\frac{\pi}{4}\right)\right\} \\ &=\tan ^{1}\left\{\tan \left(-\frac{\pi}{4}\right)\right\} \\ &=\frac{-\pi}{4} \end{aligned}

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