The numerical value of 11 + ^2 + 31 + ta n^2 + 2 ^2 will be?

Answer: Option D

$$\begin{array}{rl}& \frac{1}{1+{\cot }^2\theta }+\frac{3}{1+\text{ta}{\text{n}}^2\theta }+2{\sin }^2\theta \\ & \Rightarrow \frac{1}{{\mathrm{cosec}}^2\theta }+\frac{3}{{\sec }^2\theta }+2{\sin }^2\theta \\ & \Rightarrow {\sin }^2\theta +3\text{co}{\text{s}}^2\theta +2{\sin }^2\theta \\ & \Rightarrow 3\left({\sin }^2\theta +\text{co}{\text{s}}^2\theta \right)\\ & \Rightarrow 3\left(1\right)\\ & \Rightarrow 3\end{array}$$