Express the product as a sum or difference.
-$\cos 5 x \cos 8 x$
A) $\frac { 1 } { 2 } ( \cos 3 x + \cos 13 x )$
B) $\frac { 1 } { 2 } ( \cos 13 x - \sin 3 x )$
C) $\frac { 1 } { 2 } ( \cos 13 x - \cos 3 x )$
D) $\cos ^ { 2 } 28 x ^ { 2 }$

Question

Quizplus · Accepted Answer

The product-to-sum formula for cosine states that $\cos A \cos B = \frac{1}{2}(\cos(A - B) + \cos(A + B))$. Applying this to $\cos 5x \cos 8x$ gives $\frac{1}{2}(\cos(5x - 8x) + \cos(5x + 8x)) = \frac{1}{2}(\cos(-3x) + \cos(13x))$. Since $\cos(-\theta) = \cos(\theta)$, this simplifies to $\frac{1}{2}(\cos 3x + \cos 13x)$.

Express the Product as a Sum or Difference cos⁡5xcos⁡8x\cos 5 x \cos 8 xcos5xcos8x

Express the Product as a Sum or Difference $\cos 5 x \cos 8 x$