Verified answer

cos^2(6x)-cos12x=0

(1+cos12x)/2 - cos12x=0

1/2+1/2cos 12 x - cos 12 x=0

1/2-1/2cos 12 x=0

1-cos 12 x=0

cos 12 x=1

12 x=2*pi*k, k є Z

x=pi/6*k, k є Z