Range of ^ - 1 , ( 1 + x^2 2 + x^2 ) is - Vidyadip

MCQ

Range of ${\sin ^{ - 1\,}}\left( {\frac{{1 + {x^2}}}{{2 + {x^2}}}} \right)$ is

A
$\left[ { - \frac{\pi }{6},\frac{\pi }{6}} \right]$
B
$\left[ {0,\frac{\pi }{2}} \right)$
C
$\left[ { - \frac{\pi }{2},\frac{\pi }{2}} \right]$
✓
$\left[ { \frac{\pi }{6},\frac{\pi }{2}} \right]$

✓

Answer

Correct option: D.

$\left[ { \frac{\pi }{6},\frac{\pi }{2}} \right]$

d
$\sin ^{-1}\left(1-\frac{1}{\left(2+x^{2}\right)}\right)$

$y=\sin ^{-1}(1)$ when $x \rightarrow \infty=\frac{\pi}{2}$

When $x=0 \Rightarrow y=\sin ^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{6}$

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