Question

If $\frac{3\pi }{2}\le x\le \frac{5\pi }{2}$, then ${\sin }^{-1}\left(\sin x\right)$ is equal to-

• A. $x$
• B. $-x$
• C. $2\pi -x$
• D. $x-2\pi$

Answer 1

The correct option is D $x-2\pi$

${\sin }^{-1}\left(\sin x\right)=x-2\pi$
As $\frac{3\pi }{2}\le x\le \frac{5\pi }{2}\Rightarrow \frac{3\pi }{2}-2\pi \le x-2\pi \le \frac{5\pi }{2}$
$\Rightarrow \frac{-\pi }{2}\le x-2\pi \le \frac{\pi }{2}$