## Precalculus (6th Edition)

$\sec^{2}\theta\cdot\csc^{2}\theta$
$\displaystyle \csc^{2}\theta+\sec^{2}\theta=\frac{1}{\sin^{2}\theta}+\frac{1}{\cos^{2}\theta}$ ... common denominator: $\cos^{2}\theta\sin^{2}\theta$ ... $=\displaystyle \frac{\cos^{2}\theta+\sin^{2}\theta}{\cos^{2}\theta\sin^{2}\theta}$ $=\displaystyle \frac{1}{\cos^{2}\theta\sin^{2}\theta}$ $=\displaystyle \frac{1}{\cos^{2}\theta}\times\frac{1}{\sin^{2}\theta}$ $=\sec^{2}\theta\cdot\csc^{2}\theta$