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How do you find the exact values of tan pi/ 8 using the half angle formula?
Refer to explanation
The half angle formula for tangent can be written as follows
##tan(theta/2)=(1-costheta)/sintheta##
Now set ##theta=pi/4## you get
##tan(pi/8)=(1-cos(pi/4))/(sin(pi/4))=(1-sqrt2/2)/(sqrt2/2)=(2-sqrt2)/sqrt2##