Question

How do you evaluate `cos (π/8)`?

Answer 1

`(2 + sqrt2)/2`

Explanation:

Use the trig identity:
`2cos^2 a = 1 + cos 2a`
`2cos ^2 (pi/8) = 1 + cos (pi/4) = 1 + sqrt2/2 = (2 + sqrt2)/2`
`cos^2 (pi/8) = (2 + sqrt2)/4`
`cos (pi/8) = sqrt(2 + sqrt2)/2` (since cos (pi/8) is positive)