Question

Cos^2 2x−cos^2 6x=sin4x sin8x please help me prove it

Answer 1

Cos² 2x = (1+cos 4x )/2
cos² 6x  = (1+cos 12x)/2
subtract to get  1/2 (cos 4x - cos 12x )   
=  1/2 (2 sin  4x sin 8x )       as cos A - cos B =  2 [ sin (A+B)/2  sin (A-B)/2 ]
so the answer