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  4. sin -1( sin (2 π/3))+ cos -1( cos (7 π/6))+ tan -1( tan (3 π/4)) is equal to :

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Q. $\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)+\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)+\tan ^{-1}\left(\tan \frac{3 \pi}{4}\right)$ is equal to :

JEE MainJEE Main 2022Inverse Trigonometric Functions

Solution:

$\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)+\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)+\tan ^{-1} \tan \left(\frac{3 \pi}{4}\right)$
$\sin ^{-1} \sin \left(\frac{2 \pi}{3}\right)=\pi-\frac{2 \pi}{3}=\frac{\pi}{3}$
$\cos ^{-1}\left(\cos \frac{2 \pi}{6}\right)=2 \pi-\frac{7 \pi}{6}=\frac{5 \pi}{6}$
$\tan ^{-1} \tan \left(\frac{3 \pi}{4}\right)=\frac{3 \pi}{4}-\pi=\frac{-\pi}{4}$
$\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)+\cos ^{-1} \cos \frac{7 \pi}{6}+\tan ^{-1} \tan \frac{3 \pi}{4}$
$=\frac{11 \pi}{12}$