Question Number 50354 by prof Abdo imad last updated on 16/Dec/18
$$\left(\left({x}\right)={a}_{{k}} \right)\:_{\mathrm{1}\leqslant{k}\leqslant{n}} \:{is}\:{a}\:{sequence}\:{of}\:{reals}\:{let} \\ $$$${p}\left({x}\right)\:=\prod_{{k}=\mathrm{1}} ^{{n}} \left({cos}\left({a}_{{k}} \right)+{xsin}\left({a}_{{k}} \right)\right) \\ $$$${if}\:{p}\left({x}\right)=\left({x}^{\mathrm{2}} +\mathrm{1}\right){q}\:+{r}\:\:\:{find}\:{q}\:{and}\:{r} \\ $$$$ \\ $$