# How to prove $\sin x=…(1+\frac{x}{3\pi})(1+\frac{x}{2\pi})(1+\frac{x}{\pi})x(1-\frac{x}{3\pi})(1-\frac{x}{2\pi})(1-\frac{x}{\pi})…$? [duplicate]

Possible Duplicate:
infinite product of sine function

Here is an other one which is more or less what Euler did in one of his proofs.

The function sinx where x∈R is zero exactly at x=nπ for each integer n. If we factorized it as an infinite product we get

How to prove $$\sin x=...(1+\frac{x}{3\pi})(1+\frac{x}{2\pi})(1+\frac{x}{\pi})x(1-\frac{x}{3\pi})(1-\frac{x}{2\pi})(1-\frac{x}{\pi})...$$

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