Answer
$sin\frac{5\pi}{4}-sin\frac{3\pi}{4}=-\sqrt 2$
Work Step by Step
$sin\frac{5\pi}{4}-sin\frac{3\pi}{4}=2~cos(\frac{\frac{5\pi}{4}+\frac{3\pi}{4}}{2})~sin(\frac{\frac{5\pi}{4}-\frac{3\pi}{4}}{2})=2~cos~\pi~sin\frac{\pi}{4}=2(-1)(\frac{\sqrt 2}{2})=-\sqrt 2$
