Question

How do you find the exact values of cos^2(pi/12) using the half angle formula?

Answer 1

`(2+sqrt3)/2`.

Explanation:

Knowing that, `(1+costheta)=2cos^2(1/2theta)`, we have,

`1+cos(pi/6)=2cos^2(1/2*pi/6), i.e.,`

`1+sqrt3/2=2cos^2(pi/12)`.

`rArr cos^2(pi/12)=(2+sqrt3)/2`.