### Simplify ^@ \sqrt { \dfrac{ 1 + \cos \theta } { 1 - \cos \theta } } + \sqrt { \dfrac{ 1 - \cos \theta } { 1 + \cos \theta } } ^@

**Answer:**

^@ 2 cosec\theta ^@

**Step by Step Explanation:**

- ^@ \begin{align} & \sqrt { \dfrac{ (1 + \cos \theta)(1 + \cos \theta) } { (1 - \cos \theta)(1 + \cos \theta) } } + \sqrt { \dfrac{ (1 - \cos \theta)(1 - \cos \theta) } { (1 + \cos \theta)(1 - \cos \theta) } } \\ = & \sqrt { \dfrac{ (1 + \cos \theta)^2 } { \sin^2 \theta } } + \sqrt { \dfrac{ (1 - \cos \theta)^2 } { \sin^2 \theta } } \\ = & \dfrac{ (1 + \cos \theta + 1 - \cos \theta) } { \sin \theta } \\ = & 2 \mathrm{cosec} \theta \\ \end{align}^@