Задание:
(cos3x+cos5x+cos7x) / (sin3x+sin5x+sin7x) -?
Решение:
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)
Знаете другой ответ?