if-pi-2n-1-n-1-n-N-then-prove-that-tan-tan2-tan3-tan-n-2n-1-

Tinku Tara June 3, 2023 Trigonometry 0 Comments

Question Number 140338 by Arzoon last updated on 06/May/21

if θ=(π/(2n+1)), n≥1, n∈N ,then prove that: tanθtan2θtan3θ∙ ∙ ∙ ∙ ∙ ∙ tan(nθ) = (√(2n+1))

$${if}\:\theta=\frac{\pi}{\mathrm{2}{n}+\mathrm{1}},\:{n}\geqslant\mathrm{1},\:{n}\in{N}\:,{then}\:{prove}\:{that}: \\ $$$${tan}\theta{tan}\mathrm{2}\theta{tan}\mathrm{3}\theta\centerdot\:\centerdot\:\centerdot\:\centerdot\:\centerdot\:\centerdot\:{tan}\left({n}\theta\right)\:=\:\sqrt{\mathrm{2}{n}+\mathrm{1}} \\ $$

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