Use a Product-To-Sum Formula to Convert the Expression to a Sum

Multiple Choice

Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. $\cos \frac { \pi } { 5 } \cos \frac { 4 \pi } { 5 }$

A) $\frac { 1 } { 2 } \left( \cos \frac { 3 \pi } { 5 } + 1 \right)$
B) $\frac { 1 } { 2 } \left( \cos \frac { 3 \pi } { 5 } - 1 \right)$
C) $1 + \sin ^ { 2 } \frac { \pi } { 5 }$
D) $- \frac { 1 } { 2 } \sin \frac { 3 \pi } { 5 }$
E) $1 - \sin ^ { 2 } \frac { \pi } { 5 }$