sin3x+sin5x=sin4x
Решите уравнение

sin3x + sin5x = sin4x2[sin((3x + 5x)/2)·cos(3x - 5x)/2)] = sin4x2sin4xcosx - sin4x = 0 sin4x(2cosx - 1) = 0sin4x = 04x = πn, n ∈ Zx = πn/4, n ∈ Z2cosx - 1 = 02cosx = 1cosx = 1/2x = ±π/3 + 2πk, k ∈ ZОтвет: x =  πn/4, n ∈ Z; ±π/3 + 2πk, k ∈ Z.