Вопрос от посетителя:
(cos3x+cos5x+cos7x)/(sin3x+sin5x+sin7x)-?
Илюха отвечает:
cos3x+cos5x+cos7x=(cos 3x +cos 7x)+cos 5x=2cos 5x cos 2x+cos 5x=cos 5x(2cos 2x+1)
sin3x+sin5x+sin7x=(sin 3x+sin 7x)+sin 5x=2sin 5xcos2x+sin 5x=sin 5x (2cos x+1)
(cos3x+cos5x+cos7x)/(sin3x+sin5x+sin7x)=(cos 5x(2cos 2x+1))/(sin 5x (2cos x+1))=
cos (5x) / sin (5x) =ctg (5x)