Identitas

LHS

\begin{equation*}
\begin{split}
& \frac{\cos 3x - \cos 5x}{\sin x - \sin 3x} \\\\
& \frac{-2 \sin \frac{1}{2} (3x + 5x) \sin \frac{1}{2} (3x - 5x) }{2 \cos \frac{1}{2} (x + 3x) \sin \frac{1}{2} (x - 3x)} \\\\
& \frac{-2 \sin 4x \sin (- x) }{2 \cos 2x \sin (- x)} \\\\
& \frac{\cancel {2} \sin 4x \cancel {\sin x} }{-\cancel {2} \cos 2x \cancel {\sin x}} \\\\
& \frac{\sin 4x }{-\cos 2x } \\\\
& \frac{2 \sin 2x  \cancel {\cos 2x}}{-\cancel{\cos 2x} } \\\\
& -2 \sin 2x \: \dotso \: {\color {red} \text{RHS}}
\end{split}
\end{equation*}