Infinite Product $\prod\limits_{k=1}^\infty\left({1-\frac{x^2}{k^2\pi^2}}\right)$

I've been looking at proofs ofEuler's Sine Expansion, that is$$\frac{\sin\left(x\right)}{x}=\prod_{k = 1}^{\infty}\left(1-\frac{x^{2}}{k^{2}\pi^{2}}\right)$$All the proofs seem to rely on Complex Analysis and Fourier Series.

Is there any more elementary proof ?.