Question

How do you evaluate `cos(pi/12)` using the half angle formula?

Answer 1

`sqrt(2 + sqrt3)/2`

Explanation:

Trig identity -->
`cos (pi/6) = sqrt3/2 = 2cos^2 (pi/12) - 1`
`2cos^2 (pi/12) = 1 + sqrt3/2 = (2 + sqrt3)/2`
`cos^2 (pi/12) = (2 + sqrt3)/4`
`cos (pi/12) = +- sqrt(2 + sqrt3)/2`.
Take the positive answer because cos (pi/12) is positive.