Express the function as a trigonometric function of x.
-$\sin 4 x$
A) $3 \sin x - 4 \sin ^ { 3 } x$
B) $1 - 8 \sin ^ { 2 } x \cos ^ { 2 } x$
C) $4 \sin x \cos ^ { 3 } x - 4 \sin ^ { 3 } x \cos x$
D) $\cos ^ { 3 } x - 3 \sin ^ { 2 } x \cos x$

Question

Quizplus · Accepted Answer

The correct answer is obtained by using the trigonometric identity for the sine of a double angle, $\sin(2x) = 2\sin(x)\cos(x)$, and then applying the double angle formula again to $\sin(2x)$ to express $\sin(4x)$ as $4 \sin x \cos ^ { 3 } x - 4 \sin ^ { 3 } x \cos x$.

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