Question

Find the values of $\tan ({\sin }^{-1}\frac{3}{5}+{\cot }^{-1}\frac{3}{2})$

Answer 1

$\tan ({\sin }^{-1}\frac{3}{5}+{\cot }^{-1}\frac{3}{2})$

$=\tan ({\tan }^{-1}\frac{3}{4}+{\tan }^{-1}\frac{2}{3})$

$=\tan \left({\tan }^{-1}\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4}.\frac{2}{3}}\right)$

$=\tan \left({\tan }^{-1}\frac{9+8}{12-6}\right)$

$=\tan \left({\tan }^{-1}\frac{17}{6}\right)=\frac{17}{6}$