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

Question

Quizplus · Accepted Answer

The product-to-sum formula for $\sin A \sin B$ is $\frac{1}{2}[\cos(A-B) - \cos(A+B)]$. Applying this formula with $A = B = \frac{\pi}{8}$, we get $\frac{1}{2}[\cos(0) - \cos(\frac{\pi}{4})]$, which simplifies to $4 - 4 \cos \frac{\pi}{4}$.

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