Answer
(a) $-\frac{\sqrt 2+\sqrt 6}{4}$
(b) $\frac{\sqrt 2-1}{2}$
Work Step by Step
(a) $cos(120°+45°)=cos~120°~cos~45°-sin~120°~sin~45°=-\frac{1}{2}\frac{\sqrt 2}{2}-\frac{\sqrt 3}{2}\frac{\sqrt 2}{2}=-\frac{\sqrt 2}{4}-\frac{\sqrt 6}{4}=-\frac{\sqrt 2+\sqrt 6}{4}$
(b) $cos~120°+cos~45°=-\frac{1}{2}+\frac{\sqrt 2}{2}=\frac{\sqrt 2-1}{2}$
