It is part of an exercise in the book Basic Homological Algebra, Chapter 2 Exercise 16.
Suppose $R$ is the subring of $C^\infty(\mathbb{R})$ of all functions with period $2\pi$, and let $I$ be the maximal ideal of $R$ consisting of all functions of $R$ taking $0$ to $0$.
How can I prove that $I$ is generated by $\sin(x)$ and any (one) function in $I$ which take nonzero value at $\pi$?