Решите уравнение

cos5x+sinxsin4x=0

Cos5x+1/2 (cos (-3x) - cos (5x)) = 0

2cos5x+cos (3x) - cos (5x) = 0

cos (5x) + cos (3x) = 0

2cos (4x) cos (2x) = 0

cos (4x) = 0

4x=pi/2+pk k∈Z

x=pi/8+pk/4

cos (2x) = 0

2x=pi/2+pn n∈Z

x=pi/4+pn/2