cos²2x – cos²6x = sin4x sin8x

L.H.S = cos²2x – cos²6x
[Using the formulae 2cos²x = 1+ cos2x]
         =
         = - (cos12x – cos4x)
         = - [cos(8x + 4x) – cos(8x - 4x)]
[Using the formulae -2sinθ sinφ = cos(θ + φ ) - cos(θ - φ )]
         =× 2 sin8x sin4x
         = sin4x sin8x