Cos4x*cos2x=cos5x*cosx

Cos(4x)*Cos(2x) = Cos(5x)*Cos(x) 1/2(Cos(2x) + Cos(6x)) - 1/2(Cos(4x) + Cos(6x)) = 0 Cos(2x) + Cos(6x) - Cos(4x) - Cos(6x) = 0 Cos(2x) - Cos(4x) = 0 -2Sin((2x + 4x)/2) * Sin((2x - 4x)/2) = 0 -2Sin(3x) * Sin(-x) = 0 2Sin(3x) * Sin(x) = 0 Sin(3x) = 0 или Sin(x) = 0 1) Sin(3x) = 0 3x = π*n, n ∈ Z x = (π*n)/3, n ∈ Z 2) Sin(x) = 0 x = π*k, k ∈ Z Ответ: x = (π*n)/3, n ∈ Z x = π*k, k ∈ Z