Prove that $\prod _{n=1}^{\infty } \left(1-\frac{x}{\pi n}\right) \left(\frac{x}{\pi n}+1\right)=\sin(x)/x$

Question

Would anyone know of a reference where the following is proved, or how best to prove it? This can be checked with Mathematica, but how about a proof?

$$\prod _{n=1}^{\infty } \left(1-\frac{x}{\pi n}\right) \left(1+\frac{x}{\pi n}\right)=\frac{\sin(x)}{x}$$