Решите тригонометрическое уравнение

cos2x+cos3x=0

Cos (a) + cos (b) = 2·cos (½ (a+b)) ·cos (½ (a-b))

cos2x + cos3x = 2*cos 5x/2 * cos (-x/2)

2*cos 5x/2 * cos (-x/2) = 0

cos 2,5x * cos (-x/2) = 0

1) cos2,5x = 0

2,5x = pi/2 + pik

x = pi/5 + (2pik) / 5, k ∈ Z

2) cos (- x/2) = 0

cos (x/2) = 0

x/2 = pi/2 + pik

x = pi + 2pik, k ∈Z