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STD 12 - 1. relation and function — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 1. relation and function1 Mark
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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