Question

Prove that ${\sin }^{-1}\frac{3}{5}+{\sin }^{-1}\frac{8}{17}={\sin }^{-1}\frac{77}{85}$

Answer 1

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

$si{n}^{-1}\{\frac{3}{5}\sqrt{1-{\left(\frac{8}{17}\right)}^2}+\frac{8}{17}\sqrt{1-{\left(\frac{3}{5}\right)}^2}\}{\sin }^{-1}\{\frac{3}{5}\times \frac{15}{17}+\frac{8}{17}\times \frac{4}{5}\}{\sin }^{-1}\left\{\frac{45+32}{85}\right\}={\sin }^{-1}\frac{77}{85}$