Use the product-to-sum formula to write the given product as a sum or difference.
$$10 \sin \frac { \pi } { 8 } \cos \frac { \pi } { 8 }$$
A) $5 \sin \frac { \pi } { 8 } + 5 \cos \frac { \pi } { 8 }$
B) $5 \sin \frac { \pi } { 4 }$
C) $5 + 5 \cos \frac { \pi } { 16 }$
D) $5 - 5 \cos \frac { \pi } { 16 }$
E) $- 5 \sin \frac { \pi } { 16 }$

Question

Quizplus · Accepted Answer

The product-to-sum formula for $\sin A \cos B$ is $\frac{1}{2}[\sin(A+B) + \sin(A-B)]$. Applying this to $10 \sin \frac{\pi}{8} \cos \frac{\pi}{8}$ gives $5 \sin \frac{\pi}{4}$, since $\frac{\pi}{8} + \frac{\pi}{8} = \frac{\pi}{4}$ and $\frac{\pi}{8} - \frac{\pi}{8} = 0$, but the $\sin(0)$ term vanishes.

Use the Product-To-Sum Formula to Write the Given Product as a Sum