Rewrite with only sin x and cos x.
-$\sin 2 x - \cos 3 x$
A) $2 \sin ^ { 2 } x \cos x - \cos ^ { 3 } x - 2 \sin x \cos x$
B) $3 \sin ^ { 2 } x \cos x - \sin ^ { 3 } x + 2 \sin x \cos x$
C) $2 \sin x \cos x + \cos x - 4 \cos x \sin ^ { 2 } x$
D) $\cos ^ { 3 } x + 2 \sin ^ { 2 } x \cos x - \sin ^ { 2 } x + 2 \sin x \cos x$

Question

Quizplus · Accepted Answer

The expression $\sin 2x - \cos 3x$ can be rewritten using trigonometric identities. $\sin 2x = 2 \sin x \cos x$ and $\cos 3x = 4 \cos^3 x - 3 \cos x$. Substituting these into the original expression gives $2 \sin x \cos x - (4 \cos^3 x - 3 \cos x)$, which simplifies to $2 \sin x \cos x + 3 \cos x - 4 \cos^3 x$. This can be further simplified by factoring out $\cos x$, resulting in $2 \sin x \cos x + \cos x - 4 \cos x (\cos^2 x)$. Since $\cos^2 x = 1 - \sin^2 x$, the expression becomes $2 \sin x \cos x + \cos x - 4 \cos x (1 - \sin^2 x)$, which matches the form of choice C.

Rewrite with Only Sin X and Cos X sin⁡2x−cos⁡3x\sin 2 x - \cos 3 xsin2x−cos3x

Rewrite with Only Sin X and Cos X $\sin 2 x - \cos 3 x$