Chapter 9 - Analytic Geometry - Section 9.5 Rotation of Axes; General Form of a Conic - 9.5 Assess Your Understanding - Page 698: 4

$\cos (\dfrac{\theta}{2}) =\sqrt {\dfrac{1+\cos \theta}{2}}$

We know that the half-angle formula for $\cos$ is: $\cos (\dfrac{x}{2}) = \pm \sqrt {\dfrac{1 +\cos x}{2}}$ Since the angle is acute, we will write it as: $\cos (\dfrac{\theta}{2}) =\sqrt {\dfrac{1+\cos \theta}{2}}$