Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. $\cos 47 ^ { \circ } \cos 43 ^ { \circ }$
A) $\frac { 1 } { 2 } \left( 1 + \sin 4 ^ { \circ } \right)$
B) $\sqrt { 2 } \cos 2 ^ { \circ }$
C) $\frac { 1 } { 2 } \cos 4 ^ { \circ }$
D) $- \frac { 1 } { 2 } \cos 4 ^ { \circ }$
E) $\frac { 1 } { 2 } \left( 1 - \sin 4 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

We can use the product-to-sum formula $\cos a \cos b = \frac{1}{2} (\cos(a-b) + \cos(a+b))$. 
Plugging in $a=47^\circ$ and $b=43^\circ$, we get: 
$$\cos 47^\circ \cos 43^\circ = \frac{1}{2}(\cos 4^\circ + \cos 90^\circ) = \frac{1}{2} \cos 4^\circ$$
since $\cos 90^\circ=0$. 
Therefore, the answer is (C), $\frac{1}{2} \cos 4^\circ$.

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