Question

How do you find the exact values of cos pi/8 using the half angle formula?

Answer 1

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

Explanation:

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`