Answer
$$\sec^{2}\theta$$
Work Step by Step
Simplify
$$\tan\theta(\cot\theta+\tan\theta)$$
Use the Reciprocal Identity
$$\cot\theta= \frac{1}{\tan\theta}$$
to obtain
$$\tan\theta\bigg(\frac{1}{\tan\theta}+\tan\theta\bigg)=1+\tan^{2}\theta.$$
Finally, use the Pythagorean Identity
$$1+\tan^{2}\theta=\sec^{2}\theta$$
to obtain
$$\tan\theta(\cot\theta+\tan\theta)=\sec^{2}\theta.$$
