Решить тригонометрическое уравнение. cos3x+√3sin3x+cosx-√3sinx=0

2(1/2сos3x+√3/2sin3x)+2(1/2cosx-√3/2sinx)=0
2cos(3x-π/3)+2cos(x+π/3)=0
cos(3x-π/3)+cos(x+π/3)=0
2cos2xcos(x-π/3)=0
cos2x=0⇒2x=π/2+πk⇒x=π/4+πk/2,k∈z
cos(x-π/3)=0⇒x-π/3=π/2+πk⇒x=5π/6+πk,k∈z