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?

You can write it as $(g(x)+\sin(x))-g(x)$ where $g(x)$ is any function with $g''(x)\geq 1$. For instance, $(x^2+\sin(x))-x^2$ as was given in the comments.
