D
using the double - angle identity
cos (2A) = cos² A - sin² A = 2cos² A - 1 = 1 - 2sin² A
the right side = 1 - 2sin² (112.5° ) with A = 22.5°
hence 2A = 2 × 22.5° = 45°
thus cos 45° = 1 - 2sin² ( 22.5°)
