Use the product-to-sum formulas to rewrite the product as a sum or difference. $10 \cos 45 ^ { \circ } \cos 20 ^ { \circ }$
A) $10 \left( \cos 25 ^ { \circ } + \cos 65 ^ { \circ } \right)$
B) $\cos 25 ^ { \circ } + \cos 65 ^ { \circ }$
C) $5 \left( \cos 65 ^ { \circ } - \cos 25 ^ { \circ } \right)$
D) $5 \left( \cos 25 ^ { \circ } + \cos 65 ^ { \circ } \right)$
E) $5 \left( \cos 65 ^ { \circ } + \sin 25 ^ { \circ } \right)$

Question

Use the product-to-sum formulas to rewrite the product as a sum or difference.   $10 \cos 45 ^ { \circ } \cos 20 ^ { \circ }$  
A)  $10 \left( \cos 25 ^ { \circ } + \cos 65 ^ { \circ } \right)$
B)  $\cos 25 ^ { \circ } + \cos 65 ^ { \circ }$
C)  $5 \left( \cos 65 ^ { \circ } - \cos 25 ^ { \circ } \right)$
D) $5 \left( \cos 25 ^ { \circ } + \cos 65 ^ { \circ } \right)$
E)  $5 \left( \cos 65 ^ { \circ } + \sin 25 ^ { \circ } \right)$

Quizplus · Accepted Answer

The product-to-sum formula for cosines is $\cos A \cos B = \frac{1}{2} [\cos(A+B) + \cos(A-B)]$. Applying this to $10 \cos 45^\circ \cos 20^\circ$, we get $5 [\cos(65^\circ) + \cos(25^\circ)]$.

Use the Product-To-Sum Formulas to Rewrite the Product as a Sum