Question

How do you use the half angle formula to simplify `cos^2(pi/12)`?

Answer 1

Half angle formula: `cos^2theta=1/2(1+cos(2theta))`. So:
`cos^2(pi/12)=1/2(1+cos(pi/6))`
but `cos(pi/6)=sqrt(3)/2` so:
`cos^2(pi/12)=1/2(1+sqrt(3)/2)=1/4(2+sqrt(3))=0.933`