Precalculus (6th Edition)

Published by Pearson

Chapter 7 - Trigonometric Identities and Equations - 7.2 Verifying Trigonometric Identities - 7.2 Exercises - Page 667: 45

Answer

$\frac{\cot\theta}{\csc\theta}=\cos\theta$

Work Step by Step

Start with the left side: $\frac{\cot\theta}{\csc\theta}$ Rewrite in terms of sine and cosine: $=\frac{\frac{\cos\theta}{\sin\theta}}{\frac{1}{\sin \theta}}$ Multiply top and bottom by $\sin\theta$ and simplify: $=\frac{\frac{\cos\theta}{\sin\theta}*\sin\theta}{\frac{1}{\sin \theta}*\sin\theta}$ $=\frac{\cos\theta}{1}$ $=\cos \theta$ Since this equals the right side, the identity has been proven.

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