SOLUTION: use the half angle formula to find the exact values of tan 3pi/8

Question 672115: use the half angle formula to find the exact values of tan 3pi/8
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
use the half angle formula to find the exact values of tan 3pi/8
.
the half-angle for tangent is:
tan(x/2) = (1-cosx)/sinx
.
tan(3pi/8)
same as:
tan((1/2)(3pi/4))
so because of half-angle for tangent:
tan((1/2)(3pi/4))
= (1-cos(3pi/4))/sin(3pi/4)
= (1-(-sqrt(2)/2))/(sqrt(2)/2) (substituted values from unit circle)
= (1+sqrt(2))/sqrt(2)
= (sqrt(2)+2)/2
= sqrt(2)/2 + 1

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