Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 209: 65


$$\frac{\cos\theta}{\sin\theta\cot\theta}=1$$ The trigonometric expression is an identity, proved by the simplification of the left side.

Work Step by Step

$$\frac{\cos\theta}{\sin\theta\cot\theta}=1$$ The left side is more complex, and we would simplify it. $$A=\frac{\cos\theta}{\sin\theta\cot\theta}$$ $$A=\frac{\cos\theta}{\sin\theta}\times\frac{1}{\cot\theta}$$ We find that we can represent $$\frac{\cos\theta}{\sin\theta}=\cot\theta$$ So, $$A=\cot\theta\times\frac{1}{\cot\theta}$$ $$A=1$$ The trigonometric expression is hence proved to be an identity.
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