The principal value of sin ^{-1}left(sin left | vedclass

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(C) We know that the range of the principal value branch of $\sin ^{-1}(x)$ is $[-\frac{\pi}{2}, \frac{\pi}{2}]$.Since $\frac{2 \pi}{3}$ does not lie

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$\frac{\pi}{3}$

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(C) We know that the range of the principal value branch of $\sin ^{-1}(x)$ is $[-\frac{\pi}{2}, \frac{\pi}{2}]$.Since $\frac{2 \pi}{3}$ does not lie in the interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$,we use the property $\sin(\pi - 	heta) = \sin(	heta)$.$\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}ight)ight) = \sin ^{-1}\left(\sin \left(\pi - \frac{\pi}{3}ight)ight)$$= \sin ^{-1}\left(\sin \left(\frac{\pi}{3}ight)ight)$$= \frac{\pi}{3}$

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

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