If $x=2\pi/2009$, then evaluate $\cos x \cos 2x \cos 3x \cdots \cos 1004x$

Asked Nov 13 '19 at 13:38

Active Nov 13 '19 at 13:45

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I have been recently trying to solve a continued product of cosines:

If $x=2\pi/2009$, then evaluate $$\cos x \cos 2x \cos 3x \cdots \cos 1004x$$

I have found formula for this which says product of this series is $\pm(1/2^n)$.

I'm recently in 11th, so please try to give this proof according to my knowledge

edited Nov 13 '19 at 13:45

Blue

asked Nov 13 '19 at 13:38

shiwans trivedi

This post lack a lot of context. First, have a look at mathjax, to improve your equations. Then add your thoughts on the problem. It'll be easier for us to help you. – Alain Remillard Nov 13 '19 at 13:44
Have a look at https://math.stackexchange.com/questions/1351337/product-of-cosines-prod-r-17-cos-left-fracr-pi15-right – Claude Leibovici Nov 13 '19 at 14:10

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