Answer
See the steps.
Work Step by Step
$\cos{(x+\dfrac{3\pi}{2})} + \cos{(x-\dfrac{3\pi}{2})} = $
$$\cos{x} \cos{\dfrac{3\pi}{2}} - \sin{x} \sin{\dfrac{3\pi}{2}} + \cos{x} \cos{\dfrac{3\pi}{2}} + \sin{x} \sin{\dfrac{3\pi}{2}}$$
$LHS = 2 \cos{x} \cos{\dfrac{3\pi}{2}} = 2 \cos{x} \times 0 = 0$
$LHS = RHS$
