how to prove $\prod_{k=1}^{p-1} \sin(\frac{\pi k}{p}) = \frac{p}{2^{p-1}}$?

Question

i found this relation whilst trying to evaluate the norm (over $\mathbb{Q}$) of $1-\zeta$ for $\zeta$ a primitive $p$-th root of unity ($p$ supposed prime) $$ \prod_{k=1}^{p-1} \sin(\frac{\pi k}{p}) = \frac{p}{2^{p-1}} $$ as yet i have no means of proving it. any suggestions?

score -1 · Accepted Answer · answered Nov 01 '14 at 15:24

-1

Kindly see this article page number $5$.

answered Nov 01 '14 at 15:24

C.S.

5,528

thanks, that looks very useful – David Holden Nov 01 '14 at 15:58
1

While information at this link may answer the question, currently this is not an answer. Please consider including the essential parts of the answer here, and provide the link for reference. – user642796 Nov 02 '14 at 04:14

how to prove $\prod_{k=1}^{p-1} \sin(\frac{\pi k}{p}) = \frac{p}{2^{p-1}}$?

1 Answers1