cos^2 pi/8-1/2

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2cos^2x-1=cos2x (trig identity). Put x=(pi)/8, then 2cos^2((pi)/8)-1=cos((pi)/4)=sqrt(2)/2, or cos^2((pi)/8)=(1+sqrt(2)/2)2=1/2+sqrt(2)/4. Take 1/2 from this and we get sqrt(2)/4=0.3536.

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