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: 11

Answer

$-\cot\theta$

Work Step by Step

$\displaystyle \tan\theta-\sec\theta\csc\theta=\frac{\sin\theta}{\cos\theta}-\frac{1}{\cos\theta}\times\frac{1}{\sin\theta}$ ... common denominator: $\cos\theta\sin\theta$ ... $=\displaystyle \frac{\sin^{2}\theta-1}{\cos\theta\sin\theta}$ $=\displaystyle \frac{-(1-\sin^{2}\theta)}{\cos\theta\sin\theta}$ $=\displaystyle \frac{-\cos^{2}\theta}{\cos\theta\sin\theta}$ $=-\displaystyle \frac{\cos\theta}{\sin\theta}$ $=-\cot\theta$
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