2 + ^2 + ^2 \, cosec\, is equal to:

Answer: Option C

$$\begin{array}{rl}& \frac{2+{\tan }^2\theta +{\cot }^2\theta }{\sec \theta .\text{cosec}\theta }\\ & =\frac{{\left(\tan \theta +\cot \theta \right)}^2}{\sec \theta .\text{cosec}\theta }\\ & =\frac{{\sin }^2\theta +{\cos }^2\theta }{\left(\sec \theta .\text{cosec}\theta \right)\left({\sin }^2\theta .{\cos }^2\theta \right)}\\ & =\sec \theta .\text{cosec}\theta \end{array}$$