Answer
$\cos 87^\circ+\cos 33^\circ=\sin 63^\circ$
Work Step by Step
Start with the left side:
$\cos 87^\circ+\cos 33^\circ$
Use the Sum-to-Product Formulas on page 560:
$=2\cos\frac{87^\circ+33^\circ}{2}\cos\frac{87^\circ-33^\circ}{2}$
Simplify:
$=2\cos\frac{120^\circ}{2}\cos\frac{54^\circ}{2}$
$=2\cos 60^\circ\cos 27^\circ$
$=2\times\frac{1}{2}\cos 27^\circ$
$=\cos 27^\circ$
Use the fact that $\sin(90^\circ-x)=\cos x$:
$=\sin(90^\circ-27^\circ)$
$=\sin 63^\circ$
Since this equals the right side, the identity has been proven.