Question

Find the value of $\tan \left[\cos ^{-1}\left(\frac{1}{2}\right)+\tan ^{-1}\left(-\frac{1}{\sqrt{3}}\right)\right]$.

Answer 1

SOLUTION : $\quad \tan \left[\cos ^{-1}\left(\frac{1}{2}\right)+\tan ^{-1}\left(-\frac{1}{\sqrt{3}}\right)\right]=\tan \left[\frac{\pi}{3}+\left(-\frac{\pi}{6}\right)\right]=\tan \left(\frac{\pi}{6}\right)=\frac{1}{\sqrt{3}}$.