Cos3x+cos5x+cos7x=0

cos3x+cos5x+cos7x=0

(cos3x+cos7x) + cos5x=0

2cos ((7x+3x) / 2) cos ((7x-3x) / 2) + cos5x=0

2cos5xcos2x+cos5x=0

1) cos5x=0 или 2) 2cos2x+1=0 (запись в виде совокупности)

(1) 5x=π/2+πn, n€Z

x=π/10 + πn/5, n€Z

(2) cos2x=-1/2

2x=±arccos (-1/2) + 2πn, n€Z

2x=±2π/3 + 2πn, n€Z

x=±π/3 + πn, n€Z