Q. Number of solutions of the equation $\left|\sin ^{-1}(\sin x)\right|=\cos x$, for $x \in\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$ is equal to
Inverse Trigonometric Functions
Solution:
As $\left|\sin ^{-1}(\sin x)\right|=|x|$, for $x \in\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$
$\therefore$ From above graph, the equation
$\left|\sin ^{-1}(\sin x)\right|=\cos x$ has two solutions, in $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$.
