Решите уравнение sin3x-cos3x=√2sinx

Разделим на√2:
1/√2 · sin3x - 1/√2 · cos3x = sinx
sin(3x - π/4) = sinx
sin(3x - π/4) - sinx = 0
2cos(2x - π/8) · sin(x - π/8) = 0
cos(2x - π/8) = 0            sin(x - π/8) = 0
2x - π/8 = π/2 + πn        x - π/8 = πk
2x = 5π/8 + πn                x = π/8 + πk
x = 5π/16 + πn/2