How to prove following statements in the simplest way: $$ \sin(x)=x\prod\limits_{n = 1}^{\infty}\Big(1-\frac{x^2}{\pi^2n^2}\Big),\quad \cos(x)=\prod\limits_{n = 1}^{\infty}\Big(1-\frac{4x^2}{\pi^2(2n-1)^2}\Big). $$ We are learning infinite products, but the teacher just gave it to us without proof. I`ve read wikipedia and that material is too hard to understand(i mean Weierstrass factorization theorem, as proof follows from it). Is there any simpler way?
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