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

Nov 12, 2014

By the half-angle identity

$\tan \left(\frac{\theta}{2}\right) = \frac{\sin \theta}{1 + \cos \theta}$,

we have

$\tan \left(\frac{\pi}{8}\right) = \frac{\sin \left(\frac{\pi}{4}\right)}{1 + \cos \left(\frac{\pi}{4}\right)} = \frac{\frac{1}{\sqrt{2}}}{1 + \frac{1}{\sqrt{2}}} = \frac{1}{\sqrt{2} + 1}$

I hope that this was helpful.