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tan-2-pi-7-tan-2-3pi-7-tan-2-5pi-7-




Question Number 171389 by cortano1 last updated on 14/Jun/22
  tan^2 ((π/7))+tan^2 (((3π)/7))+tan^2 (((5π)/7))=?
$$\:\:\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\pi}{\mathrm{7}}\right)+\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)+\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{5}\pi}{\mathrm{7}}\right)=? \\ $$
Commented by Shrinava last updated on 14/Jun/22
Or sec^2  (π/7) + sec^2  ((3π)/7) + sec^2  ((5π)/7) = 21
$$\mathrm{Or}\:\mathrm{sec}^{\mathrm{2}} \:\frac{\pi}{\mathrm{7}}\:+\:\mathrm{sec}^{\mathrm{2}} \:\frac{\mathrm{3}\pi}{\mathrm{7}}\:+\:\mathrm{sec}^{\mathrm{2}} \:\frac{\mathrm{5}\pi}{\mathrm{7}}\:=\:\mathrm{21} \\ $$

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