The least value of tan2x + cot2x is?

Answer: Option B

$$\text{ta}{\text{n}}^{2}x+\text{co}{\text{t}}^{2}x$$
We know that the value of tan²x and cot²x is minimum at 45°
$$\begin{array}{rl}& \therefore \text{ta}{\text{n}}^{2}45^{\circ }+\text{co}{\text{t}}^{2}45^{\circ }\\ & =1+1\\ & =2\end{array}$$