The principal value of $\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$ is

The principal value of $\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$ is
  1. $-\left(\frac{2 \pi}{3}\right)$
  2. $\left(\frac{5 \pi}{3}\right)$
  3. $\left(\frac{\pi}{3}\right)$
  4. $\left(\frac{2 \pi}{3}\right)$

Solution

$\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)=\sin ^{-1}\left(\sin \left(\pi-\frac{2 \pi}{3}\right)\right)=\sin ^{-1}\left(\sin \left(\frac{\pi}{3}\right)\right)=\frac{\pi}{3}$

Asked in: MHT CET 2022 (06 Aug Shift 2)

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