Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 4 - Section 1.5 - More on Identities - 1.5 Problem Set - Page 47: 77


Showed that given statement, $\sin\theta\tan\theta + \cos\theta$ = $\sec\theta$, is an identity as left side transforms into right side.

Work Step by Step

Given statement is- $\sin\theta\tan\theta + \cos\theta$ = $\sec\theta$ Left Side = $\sin\theta\tan\theta + \cos\theta$ = $\sin\theta\times\frac{\sin\theta}{\cos\theta} + \cos\theta$ (Using ratio identity for $\tan\theta$) =$\frac{\sin^{2}\theta}{\cos\theta} + \cos\theta. \frac{\cos\theta}{\cos\theta} $ =$\frac{\sin^{2}\theta}{\cos\theta} + \frac{\cos^{2}\theta}{\cos\theta} $ =$\frac{\sin^{2}\theta + \cos^{2}\theta}{\cos\theta}$ =$\frac{1}{\cos\theta}$ = $\sec\theta$ = Right Side i.e. Left Side transforms into Right Side i.e. Given statement, $\sin\theta\tan\theta + \cos\theta$ = $\sec\theta$, is an identity.
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