# 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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## marked as duplicate by Norbert, Argon, Martin Sleziak, Chris Eagle, Ｊ. Ｍ.Oct 18 '12 at 8:06

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## 1 Answer

Courtesy of Edmund Landau, from his Differential and Integral Calculus.

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I don't have that book, and which part of a usual book on Mathematical Analysis could I find the proof in,like Zorich's 《Mathematical Analysis》 or ГригорийМихайлович Фихтенгольц‘s 《Calculus course》. I mean what topic it is included in? –  Miao Oct 17 '12 at 23:36
I need theorem 233 –  Lucas Zanella Sep 18 '13 at 4:01
@LucasZanella You can google the book, it is called "Differential and Integral Calculus" by Edmund Landau. –  Pedro Tamaroff Sep 18 '13 at 4:19