Perform the indicated operations and simplify the result so there are no quotients.
Solve the problem.
-$\cos 4 x$
A) $3 \sin x - 4 \sin ^ { 3 } x$
B) $4 \sin x \cos ^ { 3 } x - 4 \sin ^ { 3 } x \cos x$
C) $\cos ^ { 3 } x - 3 \sin ^ { 2 } x \cos x$
D) $\cos ^ { 4 } x - 6 \sin ^ { 2 } x \cos ^ { 2 } x + \sin ^ { 4 } x$

Question

Quizplus · Accepted Answer

The correct answer is derived from the double angle formulas and the power-reduction formulas. The expression for $\cos 4x$ can be simplified using the double angle formula for cosine, $\cos 2x = 2\cos^2 x - 1$, applied twice or directly using the formula for $\cos 4x$, which is $\cos^4 x - 6\sin^2 x \cos^2 x + \sin^4 x$. This matches choice D.

Perform the Indicated Operations and Simplify the Result So There cos⁡4x\cos 4 xcos4x

Perform the Indicated Operations and Simplify the Result So There $\cos 4 x$