sqrt(cos a+1)/(1-cos a)
I did (not sure how to format the final answer but the numerator should be sqrt'd. $$\sqrt{\frac{{\cos a +1}}{1-\cos a}}=\sqrt{\frac{{\cos a +1}}{1-\cos a}\frac{{\cos a +1}}{1+\cos a}}=\left|\frac{1+\cos a}{\sin a}\right|$$ Thanks to gimusi for formatting.
Is that correct?
It is a correct way to simplify, indeed $$\sqrt{\frac{{\cos a +1}}{1-\cos a}}=\sqrt{\frac{{\cos a +1}}{1-\cos a}\frac{{\cos a +1}}{1+\cos a}}=\left|\frac{1+\cos a}{\sin a}\right|$$
Note also that since for the existence of square root we need
$$\cos a\neq 1 \quad\land\quad \frac{{\cos a +1}}{1-\cos a}\ge0\implies -1\le\cos a<1$$
thus we can write
$$\sqrt{\frac{{\cos a +1}}{1-\cos a}}=\frac{1+\cos a}{|\sin a|}$$