Sin3x+sin5x=sin4x

Решите уравнение

Sin3x + sin5x = sin4x

2[sin ((3x + 5x) / 2) ·cos (3x - 5x) / 2) ] = sin4x

2sin4xcosx - sin4x = 0

sin4x (2cosx - 1) = 0

sin4x = 0

4x = πn, n ∈ Z

x = πn/4, n ∈ Z

2cosx - 1 = 0

2cosx = 1

cosx = 1/2

x = ±π/3 + 2πk, k ∈ Z

Ответ: x = πn/4, n ∈ Z; ±π/3 + 2πk, k ∈ Z.