trig
posted by Omar .
Find the exact value by using a halfangle identity. cos 22.5 degrees

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