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