sinx+sin2x+sin3x+sin4x=0

(sinx+sin4x)+(sin2x+sin3x)=02sin(5x/2)cos(3x/2)+2sin(5x/2)cos(x/2)=02cos(x/2)*(sin(5x/2)+sin(3x/2))=04cos(x/2)*sin(2x)cos(x/2)=04cos²(x/2)*sin(2x)=0cos(x/2)=0x/2=π/2+πkx=π+2πk,k∈zsin2x=0⇒2x=πk⇒x=πk/2,k∈z