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 $12 \sin \frac{\pi}{6} \cos \frac{\pi}{6}$, we get $6[\sin(\frac{\pi}{6} + \frac{\pi}{6}) + \sin(\frac{\pi}{6} - \frac{\pi}{6})]$, which simplifies to $6 \sin \frac{\pi}{3} + 6 \sin 0$.

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