Answer
$ 0$
Work Step by Step
$cos(-\frac{5\pi}{4})-cos\frac{3\pi}{4}\\=cos(\frac{5\pi}{4})-cos\frac{3\pi}{4}\\=cos(\pi+\frac{\pi}{4})-cos(\pi-\frac{\pi}{4})\\=-cos\frac{3\pi}{4}+cos\frac{3\pi}{4}\\=0$
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