If sin7x = cos11x, then the value of tan9x + cot9x is?

Solution (By Examveda Team)

$$\eqalign{ & \Rightarrow \sin {\text{ }}7x = \cos 11x \cr & \Rightarrow 7x + 11x = {90^ \circ } \cr & \Rightarrow 18x = {90^ \circ } \cr & \Rightarrow x = {5^ \circ } \cr & \Rightarrow \tan 9x + \cot 9x \cr & \Rightarrow \tan {45^ \circ } + \cot {45^ \circ } \cr & \Rightarrow 1 + 1 \cr & \Rightarrow 2 \cr} $$