Express the sum or difference as a product.
-$\cos 2 x - \cos 4 x$
A) $2 \sin 3 x \sin x$
B) $- 2 \sin 3 x \sin x$
C) $- 2 \cos 3 x \sin x$
D) $\cos ( - 2 x )$

Question

Quizplus · Accepted Answer

The expression $\cos 2x - \cos 4x$ can be expressed as a product using the sum-to-product identities. Specifically, the identity $\cos A - \cos B = -2 \sin \left(\frac{A + B}{2}\right) \sin \left(\frac{A - B}{2}\right)$ applies here. Substituting $A = 2x$ and $B = 4x$, we get $-2 \sin \left(\frac{2x + 4x}{2}\right) \sin \left(\frac{2x - 4x}{2}\right) = -2 \sin(3x) \sin(-x)$. Since $\sin(-x) = -\sin(x)$, the expression simplifies to $2 \sin 3x \sin x$.

Express the Sum or Difference as a Product cos⁡2x−cos⁡4x\cos 2 x - \cos 4 xcos2x−cos4x

Express the Sum or Difference as a Product $\cos 2 x - \cos 4 x$