Answer
$\frac{\sqrt3-1}{2\sqrt2}$
Work Step by Step
Using the given formula and the known values: $\cos75^\circ=\cos30^\circ\cos45^\circ-\sin30^\circ\sin45^\circ=\frac{\sqrt3}{2}\frac{1}{\sqrt2}-\frac{1}{2}\frac{1}{\sqrt2}=\frac{\sqrt3-1}{2\sqrt2}$
