tan 1 - cot + cot 1 - tan is equal to?

Answer: Option D

$$\begin{array}{rl}& \frac{\text{tan}\theta }{1-\text{cot}\theta }+\frac{\text{cot}\theta }{1-\text{tan}\theta }\\ & \Rightarrow \frac{\text{tan}\theta }{1-\frac{1}{\tan \theta }}+\frac{\frac{1}{\tan \theta }}{1-\text{tan}\theta }\\ & \Rightarrow \frac{\text{ta}{\text{n}}^2\theta }{\text{tan}\theta -1}+\frac{1}{\text{tan}\theta \left(1-\tan \theta \right)}\\ & \Rightarrow \frac{{\text{tan}}^2\theta }{\text{tan}\theta -1}-\frac{1}{\text{tan}\theta \left(\tan \theta -1\right)}\\ & \Rightarrow \frac{\text{ta}{\text{n}}^3\theta -1}{\text{tan}\theta \left(\tan \theta -1\right)}\\ & \Rightarrow \frac{\left(\text{tan}\theta -1\right)\left(\text{ta}{\text{n}}^2\theta +\text{tan}\theta +\text{1}\right)}{\text{tan}\theta \left(\tan \theta -1\right)}\\ & \Rightarrow \frac{\text{ta}{\text{n}}^2\theta +\text{tan}\theta +\text{1}}{\text{tan}\theta }\\ & \Rightarrow \text{tan}\theta +\cot \theta +\text{1}\end{array}$$