If tanθ + cotθ = -2, then the value of tan9θ + cot9θ is:

Answer: Option A

$$\begin{array}{rl}& \tan \theta +\cot \theta =-2\\ & \Rightarrow \tan \theta +\frac{1}{\tan \theta }=-2\\ & \Rightarrow \tan \theta =-1\\ & \Rightarrow {\tan }^9\theta +{\cot }^9\theta \\ & ={\tan }^9\theta +\frac{1}{{\tan }^9\theta }\\ & ={\left(-1\right)}^9+\frac{1}{{\left(-1\right)}^9}\\ & =-1-1\\ & =-2\end{array}$$