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

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1.Relation and Function

normal

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

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

D

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

Solution

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

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

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

Standard 12

Mathematics

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