The principal solution of ^ -1 ( (5 3 ) ) is - Vidyadip

MCQ

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

A
$\frac{4 \pi}{3}$
B
$\frac{5 \pi}{3}$
C
$\frac{-5 \pi}{3}$
D
$\frac{-\pi}{3}$

✓

Answer

$
\begin{array}{l}
\text { (d): In }\left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \\
\sin ^{-1}\left(\sin \left(\frac{5 \pi}{3}\right)\right)=\sin ^{-1}\left(\sin \left(2 \pi-\frac{\pi}{3}\right)\right) \\
=\sin ^{-1}\left(\sin \left(\frac{-\pi}{3}\right)\right)=\frac{-\pi}{3}
\end{array}
$

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