Half Angle Formulas/Cosine/Proof 2

Proof
Define:
 * $u = \dfrac \theta 2$

Then:

We also have that:
 * In quadrant $\text I$, and quadrant $\text {IV}$, $\cos \dfrac \theta 2 > 0$
 * In quadrant $\text {II}$ and quadrant $\text {III}$, $\cos \dfrac \theta 2 < 0$.