JEE Main 2022 (Online) 27th June Morning ShiftQuestion 1
$\sin^{-1}\left(\sin\frac{2\pi}{3}\right)+\cos^{-1}\left(\cos\frac{7\pi}{6}\right)+\tan^{-1}\left(\tan\frac{3\pi}{4}\right)$ is equal to :
Inverse Trigonometric Functions
Solution
$\sin^{-1}\sin\frac{2\pi}3=\sin^{-1}\sin\frac\pi3=\frac\pi3$. $\cos^{-1}\cos\frac{7\pi}6=\cos^{-1}\cos\frac{5\pi}6=\frac{5\pi}6$. $\tan^{-1}\tan\frac{3\pi}4=\tan^{-1}\tan(-\frac\pi4)=-\frac\pi4$. Sum $=\frac{4+10-3}{12}\pi=\frac{11\pi}{12}$. Option (A).