The set of smooth functions is dense in H

Question

Let $$C_c^\infty([a,b],\mathbb{C}):=\{f\in C^\infty([a,b],\mathbb{C}): f^{(k)}(a)=f^{(k)}(b)=0, k=0,1,...\}$$ Then $C_c^\infty([a,b],\mathbb{C})$ is dense in the Hilbert Space. Can anyone give me some tips in order to prove this theorem? How can one approach this problem?