Question

$$\frac { \frac { 1 } { \sqrt { 2 } } } { \sqrt { \frac { 1 + \cos \theta } { 1 - \cos \theta } } }$$

Evaluate

$\frac{\sqrt{2\left(\tan(\frac{\theta }{2})\right)^{2}}}{2}$

Differentiate w.r.t. θ

$\frac{\sin(\theta )\sqrt{\frac{2}{-\left(\cos(\theta )\right)^{2}+1}}\left(\sqrt{\left(-\cos(\theta )+1\right)\left(-\left(\cos(\theta )\right)^{2}+1\right)}+\left(\cos(\theta )+1\right)^{\frac{3}{2}}\right)}{4\left(\cos(\theta )+1\right)^{\frac{3}{2}}}$