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: 65

Answer

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

Work Step by Step

Given statement is- $ \cos\theta\tan\theta$ = $\sin\theta$ Now, Left Side = $ \cos\theta\tan\theta$ = $ \cos\theta.\frac{\sin\theta}{\cos\theta}$ (Using ratio identity) = $\sin\theta$ ( As $\cos\theta$ cancels out $\cos\theta$ ) = Right Side Thus proved that- Left Side = Right Side i.e. Given statement, $ \cos\theta\tan\theta$ = $\sin\theta$, is an identity.
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