Question

The value of $6\tan [{\sin }^{-1}\left(\frac{3}{5}\right)+{\cos }^{-1}\left(\frac{3}{\sqrt{13}}\right)]$ is

Answer 1

$\tan [{\sin }^{-1}\left(\frac{3}{5}\right)+{\cos }^{-1}\left(\frac{3}{\sqrt{13}}\right)]=\tan ({\tan }^{-1}\frac{3}{4}+{\tan }^{-1}\frac{2}{3})=\tan \left[{\tan }^{-1}\left(\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4}\times \frac{2}{3}}\right)\right]=\tan \left[{\tan }^{-1}\frac{17}{6}\right]=\frac{17}{6}$