Question

Помогите, пожалуйста Cos3x - Cosx = 4Cos2x

Answer 1

cosx + cos3x = 4cos2x

2*[cos(x+3x)/2]*[cos(x-3x)/2] = 4 cos2x

2*cos2x*cosx - 4cos2x = 0

2*cos2x(cosx - 2) = 0

1) 2cos2x = 0

cos2x = 0

2x = π/2 + πk, k∈Z

x = π/4 + πk/2, k∈Z

2) cosx - 2 = 0

cosx = 2 не удовлетворяет условию IcosxI ≤ 1

Ответ: x = π/4 + πk/2, k∈Z