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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
The value of $\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)+2 \cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$ :
  • A
    $\frac{\pi}{2}$
  • B
    $\frac{\pi}{3}$
  • ✓
    $\frac{2 \pi}{3}$
  • D
    $\pi$
✓

Answer

Correct option: C.
$\frac{2 \pi}{3}$
(C)
The range of principal value branch of $\sin ^{-1} x$ is $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$ and the range of principal value branch of $\cos ^{-1} x$ is $[0, \pi]$.
$\therefore \sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)=\frac{\pi}{3}$ and $\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)=\frac{\pi}{6}$
Hence, $\frac{\pi}{3}+2 \times \frac{\pi}{6}=\frac{\pi}{3}+\frac{\pi}{3}=\frac{2 \pi}{3}$
Hence correct option is (C)

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