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

Explanation

\begin{aligned}
&\text { Let } \cos ^{-1} \frac{12}{13}=x \\ \\
&\therefore \cos x=\frac{12}{13} \\ \\
&\therefore \sin x=\frac{5}{13} \\ \\
&\text { and let } \sin ^{-1} \frac{3}{5}=y \\ \\
&\sin y=\frac{3}{5} \\ \\
&\therefore \cos y=\frac{4}{5} \\ \\
&\therefore \text { using } \sin ^{x}(x)=\sin x \cos y+\cos x \sin y \\ \\
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