To find product $\cos{\theta}\cos{2\theta}\cos{3\theta}...\cos{999\theta}$

Asked Feb 09 '17 at 06:32

Active Feb 09 '17 at 06:32

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How to find out value of product

$$\cos{\theta}\cos{2\theta}\cos{3\theta}...\cos{999\theta}$$ where

$\theta=\frac{2\pi}{1999}$

i tried to multiply and divide by sin\theta to convert to sin2A, but couldnot do it. i would like to know many methods, if possible, to do this question

thanks

asked Feb 09 '17 at 06:32

Taylor Ted

3,408

Well, whatever it is, it must be EXTREMELY close to zero. – Saketh Malyala Feb 09 '17 at 06:41
@Rohan How do you find duplicates so fast? – S.C.B. Feb 09 '17 at 06:48
@S.C.B Fast?? I found it 14 minutes after the OP posted the question. Just search the site, sir. – Feb 09 '17 at 06:51
@Rohan I couldn't find it when I searched the site. – S.C.B. Feb 09 '17 at 06:52
@S.C.B Sir, put this in the search box: Find the value of $\cos x \cos 2x – Feb 09 '17 at 06:53
@Rohan How do you know to put that? I put in $\cos{\theta}\cos{2\theta}\cos{3\theta}...\cos{999\theta}$ – S.C.B. Feb 09 '17 at 06:54
@dxiv odd angles are left out – Taylor Ted Feb 09 '17 at 07:26
@TaylorTed I spoke too hastily, thanks for the correction. – dxiv Feb 09 '17 at 07:28

To find product $\cos{\theta}\cos{2\theta}\cos{3\theta}...\cos{999\theta}$

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