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Find the principal value of each of the following :

Question:

Find the principal value of each of the following :

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

Solution:

$\sin ^{-1}\left(\frac{-1}{2}\right)=-\sin ^{-1}\left(\frac{1}{2}\right)$ [Formula: $\sin ^{-1}(-x)=\sin ^{-1}(x)$ ]

$=-\frac{\pi}{6}$

 

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