If 0° < A < 90°, then the value of tan²A + cot²A - sec²A cosec²A is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{ta}}{{\text{n}}^2}{\text{A}} + {\text{co}}{{\text{t}}^2}{\text{A}} - {\sec ^2}{\text{A}}{\text{.cose}}{{\text{c}}^2}{\text{A}} \cr & {\bf{Shortcut\,\, method:}} \cr & {\text{Put A}} = {45^ \circ } \cr & \Rightarrow {\text{ta}}{{\text{n}}^2}{45^ \circ } + {\text{co}}{{\text{t}}^2}{45^ \circ } - {\sec ^2}{45^ \circ }{\text{.cose}}{{\text{c}}^2}{45^ \circ } \cr & \Rightarrow 1 + 1 - {\left( {\sqrt 2 } \right)^2}{\left( {\sqrt 2 } \right)^2} \cr & \Rightarrow - 2 \cr} $$