Answer
$$\sin2x=2\sin x\cos x$$
By writing $2x$ as the sum of $x$ and $x$ and apply the sine sum identity, the left side can be shown to be equal to the right side and therefore, the equation is an identity.
Work Step by Step
$$\sin2x=2\sin x\cos x$$
We start from the left side first.
$$X=\sin2x$$
We write $2x$ as the sum of $x$ and $x$ then apply the sine sum identity, which states
$$\sin(A+B)=\sin A\cos B+\cos A\sin B$$
$$X=\sin(x+x)$$
$$X=\sin x\cos x+\cos x\sin x$$
$$X=2\sin x\cos x$$
Therefore, 2 sides are shown to be equal. The equation thus is an identity.
