Answer
$cos~\frac{\pi}{16}~cos~\frac{3\pi}{16}-sin~\frac{\pi}{16}~sin~\frac{3\pi}{16}=\frac{\sqrt 2}{2}$
Work Step by Step
$cos(u+v)=cos~u~cos~v-sin~u~sin~v$
$cos~\frac{\pi}{16}~cos~\frac{3\pi}{16}-sin~\frac{\pi}{16}~sin~\frac{3\pi}{16}=cos(\frac{\pi}{16}+\frac{3\pi}{16})=cos~\frac{4\pi}{16}=cos~\frac{\pi}{4}=\frac{\sqrt 2}{2}$
