2011/087) Prove Cos^4x =(1/8)(3+4cos2x+cos4x)

realizing that RHS has got cos of multiple of x

Cos^4x = 1/4(2 cos ^2 x )^2
= 1/4( cos 2x + 1)^2 knowing cos 2x = 2 cos^2 x - 1
= 1/4( cos^2 2x + 2 cos 2x + 1)
= 1/8( 2 cos ^2 2x + 4 cos 2x + 2)
= 1/8( cos 4x +1 + 4 cos 2x + 2) as 2 cos^2 2x - 1 = cos 4x)]
= 1/8( cos 4x + 4 cos 2x + 3)