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