How do you use the half angle identity to find $tan (pi/8)$ ?

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Answer 1 · 2014-11-12T17:42:35

By the half-angle identity

$tan(theta/2)={sin theta}/{1+cos theta}$ ,

we have

$tan(pi/8)={sin(pi/4)}/{1+cos(pi/4)}={1/sqrt{2}}/{1+1/sqrt{2}}=1/{sqrt{2}+1}$

I hope that this was helpful.

How do you use the half angle identity to find tan (pi/8)tan (pi/8)?