Sin3x=sin2x+sinx
3sinx-4sin³x=2sinx cosx+sinx
3sinx-4sin³-2sinx cosx-sinx=0
sinx(3-4sin²x-2cosx-1)=0
sinx(-4sin²x-2cosx+2)=0
sinx(-4(1-cos²x)-2cosx+2)=0
sinx(-4+4cos²x-2cosx+2)=0
sinx(4cos²x-2cosx-2)=0
sinx=0, 4cos²x-2cosx-2=0
x=πn,n∈z замена cosx=y
4y²-2y-2=0
2y²-y-1=0
Д=1+8=9
y1=1
y2=-1/2⇒cosx=1;x=2πn
cosx=-1/2;x=+-arccos(-1/2)+2πn,n∈z;x=+-2π/3 +2πn,n∈z
Ответ:[x=πn,x=2πn,x=+-2π/3+2πn],n∈z