The value of $ an \left(\cos ^{-1}\left(\frac{4}{5} ight)+ an ^{-1}\left(\frac{2}{3} ight) ight)$ is

Question

The value of $	an \left(\cos ^{-1}\left(\frac{4}{5}ight)+	an ^{-1}\left(\frac{2}{3}ight)ight)$ is

Aicharya · Accepted Answer

$	an \left(\cos ^{-1} \frac{4}{5}+	an ^{-1} \frac{2}{3}ight)=	an \left(	an ^{-1} \frac{3}{4}+	an ^{-1} \frac{2}{3}ight)$ $=	an 	an ^{-1}\left(\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4} 	imes \frac{2}{3}}ight)=	an 	an ^{-1}\left(\frac{17}{6}ight)=\frac{17}{6}$

The value of $\tan \left(\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)$ is

Solution