Prove that if $A$ is algebra generated by $\sin(x)$ and $\cos(x)$ then $A = \{ f\in C_b(\mathbb R ) : f(t) = f(t + 2\pi )$ for all $t \in \mathbb R\}$

Question

Possible Duplicate:
Finding a closed subalgebra generated by functions.

Let $A$ be the uniformly closed subalgebra of $C_b(\mathbb{R} )$ generated by $\sin(x)$ and $\cos(x)$.

Prove: $A = \{ f\in C_b(\mathbb{R} ) : f(t) = f(t + 2\pi )$ for all $t \in \mathbb{R} \} $.