Answer
$cos\frac{3\pi}{4}-cos\frac{\pi}{4}=-\sqrt 2$
Work Step by Step
$cos\frac{3\pi}{4}-cos\frac{\pi}{4}=-2~sin(\frac{\frac{3\pi}{4}+\frac{\pi}{4}}{2})~sin(\frac{\frac{3\pi}{4}-\frac{\pi}{4}}{2})=-2~sin\frac{\pi}{2}~sin\frac{\pi}{4}=-2(1)(\frac{\sqrt 2}{2})=-\sqrt 2$
