Question

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

• A. 0
• B. 2
• C. 4
• D. 6

Answer 1

Answer: (B)

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 $\left[\frac{-\pi }{2},\frac{\pi }{2}\right]$.