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  • Need solution for RD Sharma maths class 12 chapter 3 Inverse Trigonometric Functions exercise  Very short answer question 19 math

Need solution for RD Sharma maths class 12 chapter 3 Inverse Trigonometric Functions exercise  Very short answer question 19 math

Answers (1)

Answer: \pi

Given:

\cos ^{-1}\left(\tan \frac{3 \pi}{4}\right)

Hint: Try to solve \tan  function first.

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

Solution:           

\begin{aligned} \cos ^{-1}\left(\tan \frac{3 \pi}{4}\right) &=\cos ^{-1}\left\{-\tan \left(\pi-\frac{3 \pi}{4}\right)\right\} \\\\ &=\cos ^{-1}\left\{\tan \left(\frac{-\pi}{4}\right)\right\} \\\\ &=\cos ^{-1}\left\{-\tan \frac{\pi}{4}\right\} \\\\ &=\cos ^{-1}(-1) \\\\ &=\cos ^{-1}(\cos \pi) \\\\ &=\pi \end{aligned}

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