Answer
See the steps.
Work Step by Step
$\sin{3x} - \sin{x} = 2 \cos{2x} \sin{x}$
$\cos{x} - \cos{3x} = -2 \sin{2x} \sin{-x} = 2 \sin{2x} \sin{x}$
$RHS = \dfrac{2 \cos{2x} \sin{x}}{2 \sin{2x} \sin{x}} = \cot{2x} = LHS$
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