Find the exact value by using a half-angle identity. cos 22.5 degrees

Answer 1

use
cos 2A = cos^2A - sin^2A
cos2A = cos^2A - (1 - cos^2A) = 2cos^2A - 1
cos 45° = 2cos^2 22.5° - 1
√2/2 + 1 = 2cos^2 22.5
√2/4 + 1/2 = cos^2 22.5°
cos 22.5° = √[ (√2 + 2)/4 ]
= √(√2 + 2) /2