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: 94

Answer

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

Work Step by Step

Given statement is- $ \cos\theta( \csc\theta + \tan\theta) $ = $\cot\theta + \sin\theta$ Left Side = $ \cos\theta( \csc\theta + \tan\theta) $ = $ \cos\theta $ $( \frac{1}{\sin\theta} +\frac{\sin\theta}{\cos\theta}) $ (Using reciprocal and ratio identities) = $ \frac{\cos\theta}{\sin\theta} +\sin\theta $ = $ \cot\theta$ + $ \sin\theta $ = Right Side i.e. Left Side transforms into Right Side i.e. Given statement,$ \cos\theta( \csc\theta + \tan\theta) $ = $\cot\theta + \sin\theta$, is an identity.
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