# How do I find the value of cos pi/12?

It is $\cos \left(\frac{\pi}{12}\right) = \frac{1}{4} \cdot \left(\sqrt{2} + \sqrt{6}\right)$
$\cos \left(\frac{\pi}{12}\right) = \cos \left(\frac{\pi}{3} - \frac{\pi}{4}\right) = \cos \left(\frac{\pi}{4}\right) \cos \left(\frac{\pi}{3}\right) + \sin \left(\frac{\pi}{4}\right) \sin \left(\frac{\pi}{3}\right) = \frac{\sqrt{2}}{2} \cdot \frac{1}{2} + \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} = \frac{1}{4} \cdot \left(\sqrt{2} + \sqrt{2} \cdot \sqrt{3}\right) = \frac{1}{4} \left(\sqrt{2} + \sqrt{6}\right)$