Помогите решить cos(3x+pi/3)-cos 3x=cos(x+pi/3)-cosx найти x

Question

Помогите решить cos(3x+pi/3)-cos 3x=cos(x+pi/3)-cosx
найти x

Answer 1

-2sin(3x+π/6)*sinπ/6=-2sin(x+π/6)*sinπ/6
sin(3x+π/6)=sin(x+π/6)
sin(3x+π/6)-sin(x+π/6)=0
2sinxcos(2x+π/6)=0
sinx=0⇒x=πn,n∈z
cos(2x+π/6)=0⇒2x+π/6=π/2+πk⇒2x=π/3+πk⇒x=π/6+πk/2,k∈z