Rewrite with only sin x and cos x.
-$\sin 3 x + \cos 3 x$
A) $2 \cos ^ { 2 } x \sin x + \sin x - 2 \sin ^ { 3 } x + \cos x - 4 \cos x \sin ^ { 2 } x$
B) $2 \sin x \cos ^ { 2 } x + \cos x + 1 - \sin ^ { 2 } x + \cos x$
C) $\sin x \cos ^ { 2 } x - \sin ^ { 3 } x + \cos ^ { 3 } x - \sin ^ { 2 } x \cos x$
D) $2 \sin x \cos ^ { 2 } x + \sin ^ { 3 } x - \cos ^ { 3 } x - 2 \sin ^ { 2 } x \cos x$

Question

Quizplus · Accepted Answer

Using trigonometric identities, $\sin 3x$ can be rewritten as $3\sin x - 4\sin^3 x$, and $\cos 3x$ as $4\cos^3 x - 3\cos x$. Combining these forms does not directly match any of the given options. However, by applying trigonometric identities and simplifying, option A is the closest to a correct expansion using only $\sin x$ and $\cos x$, despite the initial approach not directly leading to this form. The correct expansion involves manipulating trigonometric identities further, but none of the options directly match the standard identities for $\sin 3x + \cos 3x$. Option A, after careful consideration, seems to be an attempt to combine and simplify these identities, but the question's phrasing and the complexity of trigonometric transformations make it challenging to directly validate without further simplification steps that are not immediately apparent from the given options.

Rewrite with Only Sin X and Cos X sin⁡3x+cos⁡3x\sin 3 x + \cos 3 xsin3x+cos3x

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