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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
If $x > 1,$ then $2\tan^{-1}\text{x}+\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)$ is equal to:
  • A
    $4\tan^{-1}\text{x}$
  • B
    $0$
  • ✓
    $\frac{\pi}{2}$
  • D
    $\pi$
✓

Answer

Correct option: C.
$\frac{\pi}{2}$
$2\tan^{-1}\text{x}+\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)$
$=2\tan^{-1}\text{x}+2\tan^{-1}\text{x}$
$\Big[\because \sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)=2\tan^{-1}\text{x}\Big]$
$=4\tan^{-1}\text{x}$

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