If tanθ + cotθ = 2, then the value if tan100θ + cot100θ is?

Answer: Option A

$$\begin{array}{rl}& \text{tan}\theta +\text{cot}\theta =2\\ & \text{Put }\theta =45^{\circ }\\ & 1+1=2\left(\text{matched}\right)\\ & \text{So, }\theta =45^{\circ }\\ & \Rightarrow \text{ta}{\text{n}}^{100}45^{\circ }+\text{co}{\text{t}}^{100}45^{\circ }\\ & \Rightarrow 1^{100}+1^{100}\\ & \Rightarrow 2\end{array}$$