half angle identity!!!!!!!!!!!!!

Question

Use half angle identity to find cos 22 1/2 deg

Answer 1

Since 22.5 is half of 45, we can use the half-angle identity for cosine:

That is cos(22.5⁰) = cos(45⁰/2)

Let us take 45⁰ as A => cos(A/2) = +/- √((1+cosA)/2)

 

Since 22.5° is in the first quadrant, then the cosine value is positive, hence we can take the positive root.

i.e, +√(2 +√2)/2.