trig
posted by
kk
.
2cos^2 22.51 (find exact value)

trig 
Steve
cos^2 θ/2 = (1 + cosθ)/2
cos^2 22.5° = (1 + cos 45°)/2
= (1 + √2/2)/2
= (2 + √2)/4

trig 
Steve
hmmph
It would help to notice that
2cos^2 θ  1 = cos 2θ
so what you have is just cos 45° = 1/√2
note that 2(2+√2)/4  1 = 1+√2/21 = √2/2 = 1/√2