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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
$\sin \left(\tan ^{-1} x\right)$, where $|x|<1$, is equal to
  • A
    $\frac{x}{\sqrt{1-x^2}}$
  • B
    $\frac{1}{\sqrt{1-x^2}}$
  • C
    $\frac{1}{\sqrt{1+x^2}}$
  • D
    $\frac{x}{\sqrt{1+x^2}}$
✓

Answer

We have, $\sin \left(\tan ^{-1} x\right)$
Let $\tan ^{-1} x=\theta \Rightarrow x=\tan \theta \Rightarrow \sin \theta=\frac{x}{\sqrt{x^2+1}}$
$\therefore \quad \sin \left(\tan ^{-1} x\right)=\sin \theta=\frac{x}{\sqrt{x^2+1}}$

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