Question:
Write the value of $\cos ^{-1}\left(\tan \frac{3 \pi}{4}\right)$.
Solution:
We have
$\cos ^{-1}\left(\tan \frac{3 \pi}{4}\right)=\cos ^{-1}\left\{-\tan \left(\pi-\frac{3 \pi}{4}\right)\right\} \quad[\because \tan (\pi-x)=-\tan x]$
$=\cos ^{-1}\left\{\tan \left(-\frac{\pi}{4}\right)\right\}$
$=\cos ^{-1}\left\{-\tan \left(\frac{\pi}{4}\right)\right\}$
$=\cos ^{-1}(-1)$
$=\cos ^{-1}(\cos \pi) \quad[\because \cos \pi=-1]$
$=\pi$
$\therefore \cos ^{-1}\left(\tan \frac{3 \pi}{4}\right)=\pi$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.