We have, L.H.S. = cos 6x = cos 2(3x)
= 2 cos2 3x – 1 [Since cos2 θ = 2 cos2 θ – 1] = 2[(4cos3x–3cosx)2] –1
= 2[16 cos6x + 9 cos2x – 24 cos4x] – 1 = 32 cos6x – 48 cos4x + 18 cos2x – 1 = R.H.S.