$$\sin2x=2\sin x\cos x$$ 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.