The principal value of $\sin ^{-1}\left(\sin \frac{3 \pi}{4}\right)$ is

Question

Aicharya · Accepted Answer

$\begin{aligned} \sin ^{-1}\left(\sin \frac{3 \pi}{4}ight) & =\sin ^{-1}\left[\sin \left(\pi-\frac{\pi}{4}ight)ight] \ & =\sin ^{-1}\left(\sin \frac{\pi}{4}ight) \ & =\frac{\pi}{4}\end{aligned}$

The principal value of $\sin ^{-1}\left(\sin \frac{3 \pi}{4}\right)$ is

Solution