The value of ^ - 1 ( 10) is - Vidyadip

MCQ

The value of ${\sin ^{ - 1}}(\sin 10)$ is

A
$10$
B
$10 - 3\pi $
✓
$3\pi - 10$
D
None of these

✓

Answer

Correct option: C.

$3\pi - 10$

c
(c) Since $3\pi < 10 < 3\pi + \frac{\pi }{2}\,\, $

$\Rightarrow \,0 < 10 - 3\pi < \frac{\pi }{2}$

$ \Rightarrow \,\,\frac{{ - \pi }}{2} < 3\pi - 10 < 0$

$ \Rightarrow \,\,{\sin ^{ - 1}}\left\{ {\sin \,(3\pi - 10)} \right\} = 3\pi - 10$.

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