Question

How do you use half angle formula to find cos 22.5?

Answer 1

Find cos (22.5 deg)

Explanation:

Call cos 22.5 = cos t --> cos 2t = cos 45 deg
Trig table --> `cos 45 = (sqrt2)/2`
Use trig identity: `cos 2t = sqrt2/2 = 2cos^2 t - 1`
`2cos^2 t = 1 + sqrt2/2 = (2 + sqrt2)/2`
`cos^2 t = (2 + sqrt2)/4`

`cos t = cos 22.5 = +- sqrt(2 + sqrt2)/2`