Express the product as a sum or difference.
-$\cos \frac { 7 x } { 2 } \cos \frac { x } { 2 }$
A) $\frac { 1 } { 2 } ( \cos 3 x + \cos 4 x )$
B) $\frac { 1 } { 4 } ( \cos 8 x - \sin 6 x )$
C) $\frac { 1 } { 4 } \cos ^ { 2 } 7 x$
D) $\frac { 1 } { 2 } ( \cos 4 x - \sin 3 x )$

Question

Quizplus · Accepted Answer

The product-to-sum formula for cosine is $\cos A \cos B = \frac{1}{2}(\cos(A - B) + \cos(A + B))$. Applying this formula to $\cos \frac{7x}{2} \cos \frac{x}{2}$, we get $\frac{1}{2}(\cos(\frac{7x}{2} - \frac{x}{2}) + \cos(\frac{7x}{2} + \frac{x}{2})) = \frac{1}{2}(\cos 3x + \cos 4x)$.

Express the Product as a Sum or Difference cos⁡7x2cos⁡x2\cos \frac { 7 x } { 2 } \cos \frac { x } { 2 }cos27x​cos2x​

Express the Product as a Sum or Difference $\cos \frac { 7 x } { 2 } \cos \frac { x } { 2 }$