Решить уравнение:cosx+cos3x=0

2 * cos((х+3х)/2) * cos((х-3х)/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.