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12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\frac{{Lim}}{{x \to 1/\sqrt 2 }}$ $\frac{{x - \cos \left( {\begin{array}{*{20}{c}}  {{{\sin }^{ - 1}}}&x  \end{array}} \right)}}{{1 - \tan \left( {\begin{array}{*{20}{c}}  {{{\sin }^{ - 1}}}&x  \end{array}} \right)}}$ is
  • A
    $\frac{1}{{\sqrt 2 }}$
  • ✓
    $-\frac{1}{{\sqrt 2 }}$
  • C
    $\sqrt 2 $
  • D
    $-\sqrt 2 $
✓

Answer

Correct option: B.
$-\frac{1}{{\sqrt 2 }}$
b
put $sin^{-1}x = \theta$
$\frac{{Lim}}{{\theta  \to \pi /4}}$$\frac{{\sin \theta  - \cos \theta }}{{1 - \tan \theta }}$ 

$=\frac{{Lim}}{{\theta  \to \pi /4}}-cos\theta$

$=-\frac{1}{\sqrt 2 }$

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