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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
The principal solution of $\sin ^{-1}\left(\sin \left(\frac{5 \pi}{3}\right)\right)$ is
  • A
    $\frac{4 \pi}{3}$
  • B
    $\frac{5 \pi}{3}$
  • C
    $\frac{-5 \pi}{3}$
  • ✓
    $\frac{-\pi}{3}$
✓

Answer

Correct option: D.
$\frac{-\pi}{3}$
$\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$
$\sin ^{-1}\left(\sin \left(\frac{5 \pi}{3}\right)\right)$
$=\sin ^{-1}\left(\sin \left(2 \pi-\frac{\pi}{3}\right)\right)$
$=\sin ^{-1}\left(\sin \left(\frac{-\pi}{3}\right)\right)$
$=\frac{-\pi}{3}$

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