Trigonometry (10th Edition)

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

Chapter 5 - Trigonometric Identities - Section 5.1 Fundamental Identities - 5.1 Exercises - Page 195: 69

Answer

$$\frac{1+\tan(-\theta)}{\tan(-\theta)}=1-\cot\theta$$

Work Step by Step

$$A=\frac{1+\tan(-\theta)}{\tan(-\theta)}$$ $$A=\frac{1}{\tan(-\theta)}+\frac{\tan(-\theta)}{\tan(-\theta)}$$ $$A=\frac{1}{\tan(-\theta)}+1$$ - Negative-angle Identity: $$\tan(-\theta)=-\tan\theta$$ $$A=-\frac{1}{\tan\theta}+1$$ - Reciprocal Identity: $$\cot\theta=\frac{1}{\tan\theta}$$ $$A=-\cot\theta+1$$ $$A=1-\cot\theta$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.