let give the polynomial p(x)=(x+1)^n −(x−1)^n with n from N^∗ 1) give the factorisation of p(x) inside C[x] 2) prove that Π_(k=0) ^(n−1) cotan(((kπ)/(2p+1)))=(1/(√(2p+1)))


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Question Number 28434 by abdo imad last updated on 25/Jan/18

$l e t g i v e t h e p o l y n o m i a l p (x) = {(x + 1)}^{n} - {(x - 1)}^{n} w i t h n$ $f r o m N^{*}$ $1) g i v e t h e f a c t o r i s a t i o n o f p (x) i n s i d e C [x]$ $2) p r o v e t h a t \prod_{k = 0}^{n - 1} c o t a n (\frac{k π}{2 p + 1}) = \frac{1}{\sqrt{2 p + 1}}$
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