Решить уравнение:cosx+cos3x=0

2 * cos ((х+3 х) / 2) * cos ((х-3 х) / 2) = 0,

cos (4x/2) * cos (-2x/2) = 0,

cos2x * cos (-x) = 0,

cos2x = 0,

2x = (π/2) + πn, nϵZ,

x = (π/2) : 2 + πn : 2, nϵZ,

x = (π/4) + πn/2, nϵZ,

или

cos (-x) = 0,

cosx = 0,

x = (π/2) + πn, nϵZ.

Ответ: (π/4) + πn/2, nϵZ или (π/2) + πn, nϵZ.