Answer
$\dfrac{\sqrt{2} - \sqrt{6}}{4}$
Work Step by Step
$\cos{(\dfrac{7 \pi }{12})} = \cos{(\dfrac{\pi}{3} + \dfrac{\pi}{4})} = \cos{\dfrac{\pi}{3}} \cos{\dfrac{\pi}{4}} - \sin{\dfrac{\pi}{3} }\sin{\dfrac{\pi}{4}}$
$\cos{(\dfrac{7 \pi }{12})} = \dfrac{1}{2} \times \dfrac{\sqrt{2}}{2} - \dfrac{\sqrt{3}}{2} \dfrac{\sqrt{2}}{2}$
$\cos{(\dfrac{7 \pi }{12})} = \dfrac{\sqrt{2} - \sqrt{6}}{4}$
