Express the product as a sum or difference.
-$\cos 3 x \cos 2 x$
A) $\frac { 1 } { 2 } ( \cos x + \cos 5 x )$
B) $\frac { 1 } { 2 } ( \cos 5 x - \sin x )$
C) $\frac { 1 } { 2 } ( \cos 5 x - \cos x )$
D) $\cos ^ { 2 } 6 \mathrm { x } ^ { 2 }$

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 formula with $A = 3x$ and $B = 2x$, we get $\frac{1}{2}(\cos(3x - 2x) + \cos(3x + 2x)) = \frac{1}{2}(\cos x + \cos 5x)$.

Express the Product as a Sum or Difference cos⁡3xcos⁡2x\cos 3 x \cos 2 xcos3xcos2x

Express the Product as a Sum or Difference $\cos 3 x \cos 2 x$