Mark the tick against the correct answer in the following:
The principal value of $\sin ^{-1}\left(\frac{-1}{2}\right)$ is
A. $\frac{-\pi}{6}$
B. $\frac{5 \pi}{6}$
C. $\frac{7 \pi}{6}$
D. none of these
To Find: The Principle value of $\sin ^{-1}\left(\frac{-1}{2}\right)$
Let the principle value be given by x
Now, let $x=\sin ^{-1}\left(\frac{-1}{2}\right)$
$\Rightarrow \sin x=\frac{-1}{2}$
$\Rightarrow \sin x=-\sin \left(\frac{\pi}{6}\right)\left(\because \sin \left(\frac{\pi}{6}\right)=\frac{1}{2}\right)$
$\Rightarrow \sin x=\sin \left(-\frac{\pi}{6}\right)(\because-\sin (\theta)=\sin (-\theta))$
$\Rightarrow x=-\frac{\pi}{4}$
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