Question

${\sin }^{-1}\frac{3}{5}+{\cos }^{-1}\frac{15}{17}={\sin }^{-1}\frac{77}{85}$

Answer 1

${\sin }^{-1}\frac{3}{5}+{\cos }^{-1}\frac{15}{17}={\sin }^{-1}\frac{77}{85}$

${\sin }^{-1}\frac{3}{5}+{\sin }^{-1}\frac{8}{17}$

${\tan }^{-1}\frac{3}{4}+{\tan }^{-1}\frac{8}{15}$

$={\tan }^{-1}\left(\frac{\frac{8}{15}+\frac{3}{4}}{1-\frac{8}{15}\times \frac{3}{4}}\right)$

$={\tan }^{-1}\left(\frac{77}{36}\right)$

$={\sin }^{-1}\left(\frac{77}{85}\right)$

$=RHS.$