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

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Konstantinos Michailidis

Jun 19, 2016

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#

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