Question

The number of real solution(s) of the equation $\sqrt{1+\cos 2x}=\sqrt{2}{\sin }^{-1}\left(\sin x\right)$, where $x\in [-\pi ,\pi ]$ is

• A. $0$
• B. $1$
• C. $2$
• D. infinite

Answer 1

The correct option is C $2$

Given $\sqrt{1+\cos 2x}=\sqrt{2}{\sin }^{-1}\left(\sin x\right)$
$\Rightarrow |\cos x|={\sin }^{-1}\left(\sin x\right)$
Drawing the graphs of both, we get


Hence, the number of solutions is $2.$