Answer
$$\csc^{2}\theta$$
Work Step by Step
Use the Reciprocal Identity:
$$\sec\theta=\frac{1}{\cos\theta}$$
and the Cotangent Identity:
$$\cot\theta=\frac{\cos\theta}{\sin\theta}$$
To obtain:
$$\sec^{2}\theta\cot^{2}\theta=\bigg(\frac{1}{\cos^{2}\theta}\bigg)\bigg(\frac{\cos^{2}\theta}{\sin^{2}\theta}\bigg)=\frac{1}{\sin^{2}\theta}$$
Use the Reciprocal Identity:
$$\csc\theta=\frac{1}{\sin\theta}$$
To obtain:
$$\sec^{2}\theta\cot^{2}\theta=\csc^{2}\theta$$
