Answer
$\dfrac{\sqrt{2}}{2}$
Work Step by Step
$\cos{\alpha} + \cos{\beta} = 2 \cos{\dfrac{\alpha+\beta}{2}} \cos{\dfrac{\alpha-\beta}{2}} $
$\cos{\dfrac{\pi}{12}} + \cos{\dfrac{7\pi}{12}} = 2 \cos{\dfrac{\pi}{3}} \cos{\dfrac{-\pi}{4}} = \dfrac{\sqrt{2}}{2}$
