Question Number 77729 by aliesam last updated on 09/Jan/20
$${prove}\:{that} \\ $$$$\int_{−\pi} ^{\pi} {cos}\left(\mathrm{2}{x}\right)\:{cos}\left(\mathrm{3}{x}\right)\:{cos}\left(\mathrm{4}{x}\right)….{cos}\left(\mathrm{2005}{x}\right){dx}>\mathrm{0} \\ $$