Statement: \\(\sin(2x) = 2\sin(x)\cos(x)\\)
Proof: The Angle Addition Formula for sine can be used:
$$\sin(2x) = \sin(x + x) = \sin(x)\cos(x) + \cos(x)\sin(x) = 2\sin(x)\cos(x)$$
That's all it takes. It's a simple proof, really.