Answer
$\tan(-\frac{2\pi}{5})$ is the answer to this exercise.
Work Step by Step
$$\cot\frac{9\pi}{10}$$
As tangent and cotangent are cofunctions, in order to write $\cot\frac{9\pi}{10}$ in terms of cofunction, we now need to find $\theta$, which must satisfy
$$\tan\theta=\cot\frac{9\pi}{10}\hspace{1cm}(1)$$
According to Cofunction Identity: $\tan\theta=\cot(\frac{\pi}{2}-\theta)$
Apply this to the equation $(1)$:
$$\cot(\frac{\pi}{2}-\theta)=\cot(\frac{9\pi}{10})$$
$$\frac{\pi}{2}-\theta=\frac{9\pi}{10}$$
$$\theta=\frac{\pi}{2}-\frac{9\pi}{10}=\frac{-4\pi}{10}=-\frac{2\pi}{5}$$
$\tan(-\frac{2\pi}{5})$ is the answer to this exercise.