The value of $ an \left(\sin ^{-1}\left(\frac{3}{5} ight)+ an ^{-1}\left(\frac{2}{3} ight) ight)$ is

Question

The value of $	an \left(\sin ^{-1}\left(\frac{3}{5}ight)+	an ^{-1}\left(\frac{2}{3}ight)ight)$ is

Aicharya · Accepted Answer

$	an \left[\sin ^{-1}\left(\frac{3}{5}ight)+	an ^{-1}\left(\frac{2}{3}ight)ight]$ $=	an \left[	an ^{-1}\left(\frac{3}{4}ight)+	an ^{-1}\left(\frac{2}{3}ight)ight]$ $\cdots\left[\because \sin ^{-1} x=	an ^{-1} \frac{x}{\sqrt{1-x^2}}ight]$ $=	an \left[	an ^{-1}\left(\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4} \cdot \frac{2}{3}}ight)ight]$ $=	an \left[	an ^{-1}\left(\frac{17}{6}ight)ight]$ $=\frac{17}{6}$

The value of $\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)$ is

Solution