Can $\sin (x)$ be represented as difference of two convex functions? In my optimization homework, I am supposed to prove that every differentiable function with Lipschitz continuous gradients can be represented as difference of two convex functions. I think I have come up with a counterexample with function $f(x) = \sin (x)$ so that this statement is not true. Can anyone help me with this problem?

The derivative of $\sin(x)$ can be written as the difference of two continuous positive functions.
