Hello i'm vietnamese me
8cos^3 (x+pi/3)= cos 3x

Hello,

Remember:

1) cos 3a=4cos^3 a -3cos a
2) cos (a+b)=cos a cos b- sin a sin b
3) cos π/3=1/2
4) sin π/3=√3 /2
5) cos (x+π/3)=cos x cos π/3 - sin x sin π/3=1/2(cos x -√3 sin x)

8 cos ^3 (x+π/3)=cos 3x
==> (cos x -√3 sin x)^3 =4cos^3 x-3cos x
==> cos ^3 x -3√3cos²x sin x+9 cos x sin² x-3√3 sin^3 x -4cos^3 x+3 cos x=0
==> -3 cos^3 x -3√3 sin x(cos²x+sin²x)+9 cos x sin² x +3 cos x=0
==>3 cos ^3 x +3√3 sin x-9 cos x sin² x -3 cos x=0
==>cos ^3 x - cos x +√3 sin x -3 cos x (1-cos² x)=0
==>cos^3 x - cos x +√3 sin x -3 cos x +3 cos^3 x=0
==>4cos^3 x-4 cos x +√3 sin x=0
==>4 cos x(cos²x-1)+√3 sin x=0
==>-4 cos x sin²x+√3 sin x=0
==>sin x(-4sin x cos x +√3)=0
==>sin x(-2sin 2x+√3)=0
==> sin x=0 or sin 2x=√3/2
==> x=kπ or 2x=π/3+2kπ or 2x=2π/3+2kπ
==> x=kπ or x=π/6+kπ or x=π/3+kπ