Express the product as a sum containing only sines or cosines.
-$$\cos \frac { 11 \theta } { 2 } \cos \frac { \theta } { 2 }$$
A) $\frac { 1 } { 4 } \cos ^ { 2 } ( 5 \theta )$
B) $\frac { 1 } { 4 } [ \cos ( 6 \theta ) - \sin ( 4 \theta ) ]$
C) $\frac { 1 } { 2 } [ \cos ( 2 \theta ) + \cos ( 3 \theta ) ]$
D) $\frac { 1 } { 2 } [ \cos ( 3 \theta ) - \sin ( 2 \theta ) ]$

Question

Quizplus · Accepted Answer

Using the product-to-sum identities, $\cos A \cos B = \frac{1}{2}[\cos(A+B) + \cos(A-B)]$, we have $A = \frac{11\theta}{2}$ and $B = \frac{\theta}{2}$. Thus, $\cos \frac{11\theta}{2} \cos \frac{\theta}{2} = \frac{1}{2}[\cos(6\theta) + \cos(5\theta)]$, which simplifies to $\frac{1}{2}[\cos(2\theta) + \cos(3\theta)]$.

Express the Product as a Sum Containing Only Sines or Cosines