Sina-sinb=2sin[(a-b)/2]*cos[(a+b)/2]
2sin(-x)cos2x=cos2xsin3x
-2sinxcos2x=cos2xsin3x
cos2xsin3x+2sinxcos2x=0
cos2x(sin3x+2sinx)=0
cos2x=0⇒⇒2x=π/2+πk⇒x=π/4+πk/2,k∈z
sin3x+2sinx=0
sin(x+2x)+2sinx=0
sinxcos2x+sin2xcosx+2sinx=0
sinxcos2x+2sinxcos²x+2sinx=0
sinx(cos2x+2cos²x+2)=0
sinx=0⇒x=πk,k∈z
2cos²x-1+2cos²x+2=0
4cos²x=-1⇒cos²x=-1/4 нет решения
Ответ x=π/4+πk/2,k∈z;x=πk,k∈z