Find value of \(\displaystyle\prod_{{{r}={1}}}{\sin{{\left({\frac{{{\left({2}{r}-{1}\right)}\pi}}{{{2}{n}}}}\right)}}}\) Where \(\displaystyle{n}\in{\mathbb{{{N}}}}\) and

Rosa Townsend

Rosa Townsend

Answered question

2022-04-07

Find value of
r=1sin((2r1)π2n)
Where nN and n>1

Answer & Explanation

glanzerjbdo

glanzerjbdo

Beginner2022-04-08Added 13 answers

{r=1}nsin(2r1)π2n=u=12n1sinuπ2nv=1n1sin2vπ2n
=u=12n1sinuπ2nv=1n1sinvπn
=F(2n)F(n)
where F(m)=v=1m1sinvπm
Now
F(m)=m2m1

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