1. The problem is to find the expression for $\sin 2x$. 2. We use the double-angle formula for sine: $$\sin 2x = 2 \sin x \cos x$$. 3. This formula states that the sine of twice an angle is twice the product of the sine and cosine of the original angle. 4. There is no further simplification unless values for $x$ are given. 5. Therefore, the expression for $\sin 2x$ is $$\sin 2x = 2 \sin x \cos x$$.