Trigonometry 7th Edition

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

Chapter 1 - Section 1.5 - More on Identities - 1.5 Problem Set - Page 46: 70


Showed that given statement, $\frac{\cos\theta}{\sec\theta}$ = $\cos^{2}\theta$, is an identity as left side transforms into right side.

Work Step by Step

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