Question Number 95164 by mr W last updated on 23/May/20
$${if}\:{a}_{{k}} =\mathrm{tan}\:\left(\theta+\frac{{k}\pi}{{n}}\right), \\ $$$${find}\:\frac{\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{a}_{{k}} }{\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}{a}_{{k}} }=? \\ $$
Commented by MJS last updated on 23/May/20
$$\mathrm{seems}\:\mathrm{to}\:\mathrm{be}\:\begin{cases}{{n}=\mathrm{4}{m}+\mathrm{1};\:{n}}\\{{n}=\mathrm{4}{m}+\mathrm{3};\:−{n}}\\{{n}=\mathrm{4}{m};\:−\frac{{n}}{\mathrm{tan}\:{n}\theta}}\\{{n}=\mathrm{4}{m}+\mathrm{2};\:\frac{{n}}{\mathrm{tan}\:{n}\theta.}}\end{cases} \\ $$$$ \\ $$
Commented by john santu last updated on 23/May/20
$$\mathrm{waww}=====.= \\ $$
Commented by Rio Michael last updated on 23/May/20
$$\mathrm{hard}\:\mathrm{one}\:\mathrm{sir},\mathrm{i}\:\mathrm{solved}\:\mathrm{such}\:\mathrm{a}\:\mathrm{problem}\:\mathrm{before} \\ $$$$\mathrm{but}\:\mathrm{this}\:\mathrm{stocks} \\ $$