Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 5 - Review Exercises - Page 242: 10

Answer

$$\csc\theta+\cot\theta=\frac{1+\cos\theta}{\sin\theta}$$

Work Step by Step

$$A=\csc\theta+\cot\theta$$ - The following identities would be used to rewrite $\csc\theta$ and $\cot\theta$. $$\csc\theta=\frac{1}{\sin\theta}\hspace{2cm}\cot\theta=\frac{\cos\theta}{\sin\theta}$$ Therefore, $$A=\frac{1}{\sin\theta}+\frac{\cos\theta}{\sin\theta}$$ $$A=\frac{1+\cos\theta}{\sin\theta}$$
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