Use the product-to-sum formula to write the given product as a sum or difference. $12 \sin \frac { \pi } { 6 } \cos \frac { \pi } { 6 }$
A) $6 - 6 \cos \frac { \pi } { 12 }$
B) $6 \sin \frac { \pi } { 6 } + 6 \cos \frac { \pi } { 6 }$
C) $6 \sin \frac { \pi } { 3 } + 6 \sin 0$
D) $6 + 6 \cos \frac { \pi } { 12 }$
E) $- 6 \sin \frac { \pi } { 12 }$

Question

Use the product-to-sum formula to write the given product as a sum or difference.   $12 \sin \frac { \pi } { 6 } \cos \frac { \pi } { 6 }$  
A)  $6 - 6 \cos \frac { \pi } { 12 }$
B) $6 \sin \frac { \pi } { 6 } + 6 \cos \frac { \pi } { 6 }$  
C) $6 \sin \frac { \pi } { 3 } + 6 \sin 0$  
D) $6 + 6 \cos \frac { \pi } { 12 }$  
E) $- 6 \sin \frac { \pi } { 12 }$

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 $12 \sin \frac{\pi}{6} \cos \frac{\pi}{6}$ gives $6 \sin \frac{\pi}{3} + 6 \sin 0$, since $\sin \frac{\pi}{6} = \frac{1}{2}$ and $\cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}$.

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