Упростить выражение: 3cos(7/4пи)+2sin(3/4пи)-sin(-9/4пи)+7cos(13/2пи)

Решите задачу:

$3cos\frac{7\pi}{4}+2sin\frac{3\pi}{4}-sin(-\frac{9\pi}{4})+7cos\frac{13\pi}{2}=3cos(\pi+\frac{3\pi}{4})+2sin(\frac{\pi}{2}+\frac{\pi}{4})\\+sin(2\pi+\frac{\pi}{4})+7cos(6\pi+\frac{\pi}{2})=-3cos\frac{3\pi}{4}+2cos\frac{\pi}{4}+sin\frac{\pi}{4}+7cos\frac{\pi}{2}=\\=-3cos(\frac{\pi}{2}+\frac{\pi}{4})+2cos\frac{\pi}{4}+sin\frac{\pi}{4}+7cos\frac{\pi}{2}=3sin\frac{\pi}{4}+2cos\frac{\pi}{4}+sin\frac{\pi}{4}+\\+7cos\frac{\pi}{2}=4sin\frac{\pi}{4}+2cos\frac{\pi}{4}+7cos\frac{\pi}{2}=$
$=4*\frac{\sqrt2}{2}+2*\frac{\sqrt2}{2}+7*0=3\sqrt2$