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: 74


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

Work Step by Step

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