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Question Number 77729 by aliesam last updated on 09/Jan/20

prove that  ∫_(−π) ^π cos(2x) cos(3x) cos(4x)....cos(2005x)dx>0

$${prove}\:{that} \\ $$ $$\int_{−\pi} ^{\pi} {cos}\left(\mathrm{2}{x}\right)\:{cos}\left(\mathrm{3}{x}\right)\:{cos}\left(\mathrm{4}{x}\right)....{cos}\left(\mathrm{2005}{x}\right){dx}>\mathrm{0} \\ $$

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