The value of

$\sin ^{-1}\left(\frac{12}{13}\right)-\sin ^{-1}\left(\frac{3}{5}\right)$

$\sin ^{-1}\left(x \sqrt{1-y^{2}}-y \sqrt{1-x^{2}}\right)$

$=\sin ^{1}\left(\frac{33}{65}\right)=\cos ^{-1}\left(\frac{56}{65}\right)=\frac{\pi}{2}-\sin ^{1}\left(\frac{56}{65}\right)$