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
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