Show that `sin^-1 (3/5)+cos^-1(12/13)=cos^-1(33/65)=sin^-1(56/65)`

Explanation

\begin{aligned}
&\text { LHS }=\cos ^{-1}( 12/13 )+\sin ^{-1}( 3/5) \\ \\
&=\sin ^{-1} \sqrt{1-\left(\frac{12}{13}\right)^{2}}+\sin ^{-1} \frac{3}{5} \\ \\
&=\sin ^{-1} \sqrt{1-\frac{144}{169}}+\sin ^{-1} \frac{3}{5} \\ \\
&=\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{3}{5} \\ \\
&=\sin ^{-1}\left[\frac{5}{13} \sqrt{1-\left(\frac{3}{5}\right)^{2}}+\frac{3}{5} \sqrt{1-\left(\frac{5}{13}\right)^{2}}\right] \\ \\
&{\left[\left(\frac{5}{13}\right)^{2}+\left(\frac{3}{5}\right)^{2} \leq 1\right]} \\ \\
&=\sin ^{-1}\left[\frac{5}{13} \sqrt{1-\frac{9}{25}}+\frac{3}{5} \sqrt{1-\frac{25}{169}}\right] \\ \\
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