If 2 x 3 2 , then ^ - 1 ( x) is equal to - Vidyadip

MCQ

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

A
$x$
B
$ - x$
C
$\pi + x$
✓
$\pi - x$

✓

Answer

Correct option: D.

$\pi - x$

d
(d) We have $\frac{\pi }{2} \le x \le \frac{{3\pi }}{2}$

$ \Rightarrow \,\,\frac{{ - \pi }}{2} \le x - \pi \le \frac{\pi }{2}\,\, \Rightarrow \,\,\frac{{ - \pi }}{2} \le \pi - x \le \frac{\pi }{2}$

$ \Rightarrow \,\,{\sin ^{ - 1}}\{ \sin \,(\pi - x)\} = \pi - x$.

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