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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
$\cos ^{-1}\left(\frac{-1}{2}\right)+2 \sin ^{-1}\left(\frac{-1}{2}\right)$ is equal to
  • ✓
    $\frac{\pi}{3}$
  • B
    $\frac{2 \pi}{3}$
  • C
    $\frac{3 \pi}{4}$
  • D
    $\frac{5 \pi}{8}$
✓

Answer

Correct option: A.
$\frac{\pi}{3}$
(a) : Principal value of $\cos ^{-1}\left(\frac{-1}{2}\right)$ is $\frac{2 \pi}{3}$
and principal value of $\sin ^{-1}\left(\frac{-1}{2}\right)$ is $\left(\frac{-\pi}{6}\right)$.
$\therefore \quad \cos ^{-1}\left(\frac{-1}{2}\right)+2 \sin ^{-1}\left(\frac{-1}{2}\right)$
$=\frac{2 \pi}{3}+\left(2 \times \frac{-\pi}{6}\right)=\frac{2 \pi}{3}-\frac{\pi}{3}=\frac{\pi}{3}$

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