SOLUTION : $\sin ^{-1}\left(\frac{8}{17}\right)+\sin ^{-1}\left(\frac{3}{5}\right)=\sin ^{-1}\left[\frac{8}{17} \sqrt{1-\frac{9}{25}}+\frac{3}{5} \sqrt{1-\frac{64}{289}}\right]$
$=\sin ^{-1}\left[\frac{8}{17} \times \frac{4}{5}+\frac{3}{5} \times \frac{15}{17}\right]=\sin ^{-1}\left[\frac{32+45}{85}\right]=\sin \left[\frac{77}{85}\right]=\cos ^{-1} \sqrt{1-\left(\frac{77}{85}\right)^2}\left[\because \sin ^{-1} \times \cos ^{-1} \sqrt{1-x^2}\right] \\$
$=\cos ^{-1} \sqrt{\frac{7225-5929}{(85)^2}}=\cos ^{-1} \sqrt{\frac{1296}{(85)^2}}=\cos ^{-1}\left(\frac{36}{85}\right)$
