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Question-18841




Question Number 18841 by mondodotto@gmail.com last updated on 30/Jul/17
Answered by Tinkutara last updated on 31/Jul/17
(√(2 + (√(2 + (√(2(1 + cos 8θ)))))))  = (√(2 + (√(2(1 + cos 4θ))))) = (√(2(1 + cos 2θ)))  = 2 cos θ
$$\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}\left(\mathrm{1}\:+\:\mathrm{cos}\:\mathrm{8}\theta\right)}}} \\ $$$$=\:\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}\left(\mathrm{1}\:+\:\mathrm{cos}\:\mathrm{4}\theta\right)}}\:=\:\sqrt{\mathrm{2}\left(\mathrm{1}\:+\:\mathrm{cos}\:\mathrm{2}\theta\right)} \\ $$$$=\:\mathrm{2}\:\mathrm{cos}\:\theta \\ $$

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