Answer
See the steps.
Work Step by Step
$\sin{4x} + \sin{6x} = 2 \sin{5x} \cos{-x} = 2 \sin{5x} \cos{x}$
$\cos{4x} - \cos{6x} = -2 \sin{5x} \sin{-x} = 2 \sin{5x} \sin{x}$
$RHS = \dfrac{2 \sin{5x} \cos{x}}{2 \sin{5x} \sin{x}} = \cot{x}= LHS$