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