The value of sin ^{-1}left(frac{-1}{2}right)+ | vedclass

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(D) We know that the range of the principal value branch of $\sin ^{-1} x$ is $[-\frac{\pi}{2}, \frac{\pi}{2}]$.First,evaluate $\sin ^{-1}\left(\frac{

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$\frac{-\pi}{2}$

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(D) We know that the range of the principal value branch of $\sin ^{-1} x$ is $[-\frac{\pi}{2}, \frac{\pi}{2}]$.First,evaluate $\sin ^{-1}\left(\frac{-1}{2}\right)$:Since $\sin(\frac{-\pi}{6}) = \frac{-1}{2}$,we have $\sin ^{-1}\left(\frac{-1}{2}\right) = \frac{-\pi}{6}$.Next,evaluate $\sin ^{-1}\left(\frac{-\sqrt{3}}{2}\right)$:Since $\sin(\frac{-\pi}{3}) = \frac{-\sqrt{3}}{2}$,we have $\sin ^{-1}\left(\frac{-\sqrt{3}}{2}\right) = \frac{-\pi}{3}$.Adding these values together:$\frac{-\pi}{6} + (\frac{-\pi}{3}) = \frac{-\pi - 2\pi}{6} = \frac{-3\pi}{6} = \frac{-\pi}{2}$.

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

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