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

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Answer 1 · 2016-06-19T18:49:54

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 $pi/8$ = $sqrt (2+sqrt2) /2$

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