The least value of tan²x + cot²x is?

Solution (By Examveda Team)

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