Matematické Fórum

stuart clark · 30. 12. 2011 17:38

Find value of $\displyatyle \cos (\theta)\times\cos (2\theta)\times\cos (3\theta)................\times\cos (999\theta) =$

If $\displaystyle \theta = \frac{\pi}{1999}$

(without using complex number)

stuart clark · 31. 12. 2011 19:49

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stuart clark · 31. 12. 2011 19:52

now my question is how can we solve using Complex number

thanks

check_drummer · 01. 01. 2012 00:48

Hi, excuse me, I don't understand following text, can you please explain it? Thank you very much.

stuart clark napsal(a):
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Skrytý text:

Using $\sin (1998 \theta) = \sin (\pi-\theta)=\sin (\theta)$

similarly $\sin (1996 \theta) = \sin (\pi-2\theta)=\sin (2\theta)$
....................................

....................................

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$\sin (\theta) = \sin (\pi-999\theta)=\sin (999\theta)$

So $2^{999}x.y = y$

stuart clark · 03. 01. 2012 11:17

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Matematické Fórum

#1 30. 12. 2011 17:38

Trigonometric Sum

#2 31. 12. 2011 19:49

Re: Trigonometric Sum

#3 31. 12. 2011 19:52

Re: Trigonometric Sum

#4 01. 01. 2012 00:48

Re: Trigonometric Sum

stuart clark napsal(a):

#5 03. 01. 2012 11:17

Re: Trigonometric Sum

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