trigonometry - Simplifying $sin(4x)cos(4x)$

Simplify $\sin(4x)\cos(4x)$ using double angle or compound trigonometry.

Can someone please show me how its done, Ive tried several times but no where near the answer.

Answer

The double angle formula is $\ 2 \sin\theta\cos\theta = \sin(2\theta) \iff \sin\theta\cos\theta = \frac{1}{2} \sin(2\theta)$.

By applying this formula with $\theta = 2x$, we obtain

$$\sin4x\cos4x=\frac{1}{2} \sin(8x).$$