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

Answer: Option B

$$\begin{array}{rl}& \Rightarrow \sin 7x=\cos 11x\\ & \Rightarrow 7x+11x=90^{\circ }\\ & \Rightarrow 18x=90^{\circ }\\ & \Rightarrow x=5^{\circ }\\ & \Rightarrow \tan 9x+\cot 9x\\ & \Rightarrow \tan 45^{\circ }+\cot 45^{\circ }\\ & \Rightarrow 1+1\\ & \Rightarrow 2\end{array}$$