Answer
The expression is $r=\frac{2}{1+\frac{\cos \theta }{2}}$
Work Step by Step
Let us consider the expression:
$\frac{4}{2+\cos \theta }$
We divide the numerator and denominator by 2.
$\begin{align}
& \frac{4}{2+\cos \theta }=\frac{{4}/{2}\;}{{2+\cos \theta }/{2}\;} \\
& =\frac{2}{1+\frac{\cos \theta }{2}}
\end{align}$
Thus, $r=\frac{2}{1+\frac{\cos \theta }{2}}$
