Write the product as a sum or difference of trigonometric functions.
-$\sin 8 x \cos 8 x$
A) $\cos 8 x$
B) $\frac { 1 } { 2 } \sin 16 x$
C) $\cos 4 x$
D) $2 \sin 4 x$

Question

Quizplus · Accepted Answer

This is an application of the double angle formula for sine, which states that $\sin(2\theta) = 2\sin(\theta)\cos(\theta)$. By setting $\theta = 8x$, we get $\sin(16x) = 2\sin(8x)\cos(8x)$, which simplifies to $\sin(8x)\cos(8x) = \frac{1}{2}\sin(16x)$.

Write the Product as a Sum or Difference of Trigonometric sin⁡8xcos⁡8x\sin 8 x \cos 8 xsin8xcos8x

Write the Product as a Sum or Difference of Trigonometric $\sin 8 x \cos 8 x$