Question

sinx+sin5x=sin3x - решить уравнение

Answer 1

Ответ:

x = πk/3, k ∈Z; x = +-π/6 + πn, n ∈ Z

Пошаговое объяснение:

sinx + sin5x = 2sin3x*cos2x = sin3x

sin3x(2cos2x - 1) = 0

sin3x = 0

3x = πk, k ∈ Z

x = πk/3, k ∈Z

2cos2x - 1 = 0

cos2x = 1/2

2x = +-π/3 + 2πn

x = +-π/6 + πn, n ∈ Z