Answer
See the steps.
Work Step by Step
$\cos{(x+\dfrac{\pi}{4})}+ \cos{(x-\dfrac{\pi}{4})} = $
$$\cos{x} \cos{\dfrac{\pi}{4}} - \sin{x} \sin{\dfrac{\pi}{4}} + \cos{x} \cos{\dfrac{\pi}{4}} + \sin{x} \sin{\dfrac{\pi}{4}}$$
$LHS = 2 \cos{x} \cos{\dfrac{\pi}{4}} = 2 \cos{x} \times \dfrac{1}{\sqrt{2}} = \sqrt{2} \cos{x}$
$LHS = RHS$
