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

MCQ

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

A
$x$
B
$ - x$
C
$2\pi + x$
✓
$2\pi - x$

✓

Answer

Correct option: D.

$2\pi - x$

d
(d) It is given that $\pi \le x \le 2\pi $

$ \Rightarrow \,\, - \pi \ge - x \ge - 2\pi \,\,\, \Rightarrow \,\,\pi \ge 2\pi - x \ge 0$

$ \Rightarrow \,\,{\cos ^{ - 1}}\,\left\{ {\cos \,(2\pi - x)} \right\} = 2\pi - x$.

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