Use Identities to find the exact value.
Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
-$\sin 4 x$
A) $\cos ^ { 3 } x - 3 \sin ^ { 2 } x \cos x$
B) $1 - 8 \sin ^ { 2 } x \cos ^ { 2 } x$
C) $4 \sin x \cos ^ { 3 } x - 4 \sin ^ { 3 } x \cos x$
D) $3 \sin x - 4 \sin ^ { 3 } x$

Question

Quizplus · Accepted Answer

The correct expression for $\sin 4x$ in terms of sine and cosine, simplified to avoid quotients, is $4 \sin x \cos ^ { 3 } x - 4 \sin ^ { 3 } x \cos x$. This is derived using the double angle formulas for sine and cosine, and then applying them again to the result.

Use Identities to Find the Exact Value sin⁡4x\sin 4 xsin4x A) cos⁡3x−3sin⁡2xcos⁡x\cos ^ { 3 } x - 3 \sin ^ { 2 } x \cos xcos3x−3sin2xcosx

Use Identities to Find the Exact Value $\sin 4 x$ A) $\cos ^ { 3 } x - 3 \sin ^ { 2 } x \cos x$