The value of $\sqrt{\frac{1+\cos \theta }{1-\cos \theta }}$  is equal to

$=\frac{1+\cos \theta }{\left|\sin \theta \right|}$

If $0<\theta <\pi$ $\frac{1+\cos \theta }{\left|\sin \theta \right|}=\cos ec\theta +\cot \theta$

If $\pi <\theta <2\pi$ $\frac{1+\cos \theta }{-\sin \theta }=-\cos ec\theta -\cot \theta$