Use a sum-to-product identity to rewrite the expression.
-cos 22° - cos 50°
A) 2 sin 36° sin 14°
B) -2 sin 36° sin 14°
C) -2 cos 36° cos 14°
D) 2 sin 36° cos 14°

Question

Quizplus · Accepted Answer

The sum-to-product identity for cosines, $\cos A - \cos B = -2 \sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)$, can be applied here with $A = 22°$ and $B = 50°$, resulting in $2 \sin 36° \sin 14°$.

Use a Sum-To-Product Identity to Rewrite the Expression