Question

How do you use the half-angle identity to find the exact value of cos(-pi/12)?

Answer 1

`sqrt(2+sqrt3)/2`

Explanation:

`cos(-pi/12)=cos(pi/12)` `as` `cos(x)` `is` `a` `even function` `f(x)=f(-x)`
`costheta=sqrt((1+cos2theta)/2)`
`=>cos(pi/12)=sqrt((1+cos(pi/6))/2)=sqrt((1+sqrt3/2)/2)=sqrt(2+sqrt3)/2`