Answer
$\frac{3(\sqrt{2}+\sqrt{3})}{4}$
Work Step by Step
Use the third Product-to-Sum Formula, $\cos u\cos v=\frac{1}{2}[\cos(u+v)+\cos(u-v)]$.
$3\cos37.5^\circ\cos7.5^\circ$
$=3\times\frac{1}{2}[\cos(37.5^\circ+7.5^\circ)+\cos(37.5^\circ-7.5^\circ)]$
$=\frac{3}{2}(\cos 45^\circ+\cos 30^\circ)$
$=\frac{3}{2}(\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{2})$
$=\frac{3}{2}(\frac{\sqrt{2}+\sqrt{3}}{2})$
$=\frac{3(\sqrt{2}+\sqrt{3})}{4}$
