Question

How do you find the value of `cos(pi/8)`?

Answer 1

The half angle formula for cosine is `cos x= 2 cos^2 (x/2) -1`.
Thus

cos `pi/4 = 2 cos^2 (pi/8) -1`,

`cos^2 (pi/8)= ( 1+ cos (pi/4))/2`

=`( 1+sqrt2)/(2sqrt2)`= `(2+sqrt2)/4`

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