Question Number 28434 by abdo imad last updated on 25/Jan/18
![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)))](Q28434.png)
$${let}\:{give}\:{the}\:{polynomial}\:{p}\left({x}\right)=\left({x}+\mathrm{1}\right)^{{n}} −\left({x}−\mathrm{1}\right)^{{n}} {with}\:{n} \\ $$$${from}\:{N}^{\ast} \\ $$$$\left.\mathrm{1}\right)\:{give}\:{the}\:{factorisation}\:{of}\:{p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} {cotan}\left(\frac{{k}\pi}{\mathrm{2}{p}+\mathrm{1}}\right)=\frac{\mathrm{1}}{\sqrt{\mathrm{2}{p}+\mathrm{1}}} \\ $$