Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - Chapter 7 Test Prep - Review Exercises: 12

Answer

$\sec^{2}\theta\cdot\csc^{2}\theta$

Work Step by Step

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