Half Angle Formulas/Cosine/Proof 2

Theorem
where $\cos$ denotes cosine.

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

Then:

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