Question

Using the principal values, evaluate the following : $\tan ^{-1} 1+\sin ^{-1}\left(-\frac{1}{2}\right)$

Answer 1

SOLUTION : We have $\tan ^{-1} 1+\sin ^{-1}\left(-\frac{1}{2}\right)=\frac{\pi}{4}-\sin ^{-1}\left(-\frac{1}{2}\right)=\frac{\pi}{4}-\frac{\pi}{6}=\frac{3 \pi-2 \pi}{12}=\frac{\pi}{12}$