Answer
See the steps.
Work Step by Step
$\cos{(\dfrac{\pi}{3}+x)} + \cos{(\dfrac{\pi}{3}-x)} = $
$$\cos{\dfrac{\pi}{3}} \cos{x} - \sin{\dfrac{\pi}{3}}\sin{x} + \cos{\dfrac{\pi}{3}} \cos{x} + \sin{\dfrac{\pi}{3}}\sin{x} $$
$LHS = 2 \cos{\dfrac{\pi}{3}} \cos{x} = 2 \times \dfrac{1}{2} \cos{x} = \cos{x}$
$LHS = RHS$
