Question

How do you use a half-angle formula to find `cos (pi/8)`?

Answer 1

The answer is: `sqrt(2+sqrt2)/2`.

The half-angle formula of cosine is:

`cos(alpha/2)=sqrt((1+cosalpha)/2)`.

In this case:

`cos(pi/8)=cos((pi/4)/2)=sqrt((1+cos(pi/4))/2)=sqrt((1+sqrt2/2)/2)=sqrt(((2+sqrt2)/2)/2)=sqrt((2+sqrt2)/4)=sqrt(2+sqrt2)/2`.