# What is the value of cos 75°?

$\frac{\sqrt{6} - \sqrt{2}}{4}$
$\cos \left(75\right) = \cos \left(30 + 45\right) = \cos 30 \cdot \cos 45 - \sin 30 \cdot \sin 45 =$
= $\left(\frac{\sqrt{3}}{2}\right) \left(\frac{\sqrt{2}}{2}\right) - \left(\frac{1}{2}\right) \left(\frac{\sqrt{2}}{2}\right) = \frac{\sqrt{6} - \sqrt{2}}{4}$