Cos 4x cos 2x = cos 5x cos x

Cos4x cos2x = cosx cosx*. Это во первых!. Cos(4x)*Cos(2x) = Cos(x)*Cos(5x) 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 :)