Answer
$\frac{\sqrt 6}{2}$
Work Step by Step
Using the Sum-to-Product Formula $cos(u)+cos(v)=2cos\frac{u+v}{2}cos\frac{u-v}{2}$, we have $cos(75^\circ )+cos(15^\circ)=2cos\frac{75^\circ+15^\circ}{2}cos\frac{75^\circ-15^\circ}{2}=2cos(45^\circ) cos(30^\circ)=2(\frac{\sqrt 2}{2})(\frac{\sqrt 3}{2})=\frac{\sqrt 6}{2}$
