Cos Sin Product
1. The problem is to understand the expression $\cos x \sin x$.
2. This is a product of the cosine and sine trigonometric functions.
3. We can express $\cos x \sin x$ using the double-angle identity for sine:
$$\sin(2x) = 2 \sin x \cos x$$
4. Therefore,
$$\cos x \sin x = \frac{\sin(2x)}{2}$$
5. So the expression $\cos x \sin x$ is equal to half of $\sin(2x)$.