Question

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

Answer 1

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
:)