Use the sum of two angles identity for the cosine:
cos(60) = cos(30+30)
cos(30+30) = cos(30)cos(30)- sin(30)sin(30)
= cos2(30) - sin2(30)
= cos2(30) - (1 - cos2(30)) [sin2x + cos2x = 1, so sin2x = 1 - cos2x)
= cos2(30) - 1 + cos2(30)
= 2cos2(30) - 1
