MCQ
The principal value of $\sin ^{-1}\left[\sin \left(\frac{2 \pi}{3}\right)\right]$ is
- A$-\frac{2 \pi}{3}$
- B$\frac{2 \pi}{3}$
- C$\frac{4 \pi}{3}$
- ✓$\frac{\pi}{3}$
✓
Answer
Correct option: D.
$\frac{\pi}{3}$
(D) The principal value of $\sin ^{-1}\left[\sin \left(\frac{2 \pi}{3}\right)\right]$
$=\sin ^{-1}\left[\sin \left(\pi-\frac{2 \pi}{3}\right)\right]=\sin ^{-1}\left[\sin \left(\frac{\pi}{3}\right)\right]=\frac{\pi}{3}$
$=\sin ^{-1}\left[\sin \left(\pi-\frac{2 \pi}{3}\right)\right]=\sin ^{-1}\left[\sin \left(\frac{\pi}{3}\right)\right]=\frac{\pi}{3}$
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