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