Use an identity to write the expression as a single trigonometric function or as a single number.
-$\sin 8 x \cos 8 x$
A) $\frac { 1 } { 2 } \sin 16 x$
B) $\cos 4 x$
C) $\cos 8 x$
D) $2 \sin 4 x$

Question

Quizplus · Accepted Answer

This expression can be simplified using the double angle identity for sine, which states that $\sin(2\theta) = 2\sin(\theta)\cos(\theta)$. By applying this identity, where $\theta = 8x$, we get $\sin(16x) = 2\sin(8x)\cos(8x)$. Therefore, to express $\sin(8x)\cos(8x)$ as a single trigonometric function, we divide both sides by 2, resulting in $\frac{1}{2}\sin(16x)$.

Use an Identity to Write the Expression as a Single sin⁡8xcos⁡8x\sin 8 x \cos 8 xsin8xcos8x

Use an Identity to Write the Expression as a Single $\sin 8 x \cos 8 x$