Chapter 7 - Trigonometric Identities and Equations - 7.2 Verifying Trigonometric Identities - 7.2 Exercises - Page 666: 38

$\sec^2\theta$

$\frac{\csc \theta\sec\theta}{\cot \theta}$ $=\frac{\frac{1}{\sin\theta}*\frac{1}{\cos \theta}}{\frac{\cos\theta}{\sin\theta}}$ $=\frac{\frac{1}{\sin\theta}*\frac{1}{\cos \theta}*\cos\theta\sin\theta}{\frac{\cos\theta}{\sin\theta}*\cos\theta\sin\theta}$ $=\frac{1}{\cos^2\theta}$ $=(\frac{1}{\cos\theta})^2$ $=\sec^2\theta$