# How do you use a half-angle formula to find cos (pi/8)?

The answer is: $\frac{\sqrt{2 + \sqrt{2}}}{2}$.
$\cos \left(\frac{\alpha}{2}\right) = \sqrt{\frac{1 + \cos \alpha}{2}}$.
$\cos \left(\frac{\pi}{8}\right) = \cos \left(\frac{\frac{\pi}{4}}{2}\right) = \sqrt{\frac{1 + \cos \left(\frac{\pi}{4}\right)}{2}} = \sqrt{\frac{1 + \frac{\sqrt{2}}{2}}{2}} = \sqrt{\frac{\frac{2 + \sqrt{2}}{2}}{2}} = \sqrt{\frac{2 + \sqrt{2}}{4}} = \frac{\sqrt{2 + \sqrt{2}}}{2}$.