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Prove that cos theta* cos 2theta* cos2^...

Prove that `cos theta* cos 2theta* cos2^(2)theta * cos2^(3)theta x... cos 2^(n-1) theta = 1/2^(n)` , when `theta = pi/(2^(n)+1)`.

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A DAS GUPTA-Circular Functions, Identities -Exercise
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  16. Sum the series: sin alpha - sin 2alpha + sin 3alpha - sin 4alpha + .....

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  17. Find sum(r=1)^(10) cos^(3) rpi/3.

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