Answer
The identity is verified.
$cos(\frac{5\pi}{4}-x)=-\frac{\sqrt 2}{2}(cos~x+sin~x)$
Work Step by Step
$cos(u-v)=cos~u~cos~v+sin~u~sin~v$
$cos(\frac{5\pi}{4}-x)=cos~\frac{5\pi}{4}~cos~x+sin~\frac{5\pi}{4}~sin~x=-\frac{\sqrt 2}{2}cos~x+(-\frac{\sqrt 2}{2})sin~x=-\frac{\sqrt 2}{2}(cos~x+sin~x)$
