Question

The number of solutions of the equation $x{\sin }^{-1}(\sin x)+x=\pi$ in $[0,2\pi ]$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

$x{\sin }^{-1}(\sin x)+x=\pi$
${\sin }^{-1}(\sin x)=\frac{\pi }{x}-1$
$f(x)={\sin }^{-1}\sin x\text{ and }g(x)=\frac{\pi }{x}-1$