Answer
(a) $-\frac{\sqrt 6-\sqrt 2}{4}$
(b) $\frac{\sqrt 2+1}{2}$
Work Step by Step
$cos(u+v)=cos~u~cos~v-sin~u~sin~v$
(a) $cos(\frac{\pi}{4}+\frac{\pi}{3})=cos~\frac{\pi}{4}~cos~\frac{\pi}{3}-sin~\frac{\pi}{4}~sin~\frac{\pi}{3}=\frac{\sqrt 2}{2}~\frac{1}{2}-\frac{\sqrt 2}{2}~\frac{\sqrt 3}{2}=\frac{\sqrt 2}{4}-\frac{\sqrt 6}{4}=\frac{\sqrt 2-\sqrt 6}{4}=-\frac{\sqrt 6-\sqrt 2}{4}$
(b) $cos~\frac{\pi}{4}+cos~\frac{\pi}{3}=\frac{\sqrt 2}{2}+\frac{1}{2}=\frac{\sqrt 2+1}{2}$
