Trigonometry (11th Edition) Clone

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

Chapter 5 - Review Exercises - Page 248: 9



Work Step by Step

$$A=\tan^2\theta(1+\cot^2\theta)$$ - For $\tan^2\theta$, we apply the identity $$\tan\theta=\frac{\sin\theta}{\cos\theta}$$ - For $1+\cot^2\theta$, we can use the identity $$1+\cot^2\theta=\csc^2\theta$$ However, we also have $\csc\theta=\frac{1}{\sin\theta}$. As such, $$1+\cot^2\theta=\frac{1}{\sin^2\theta}$$ Replace all back to $A$: $$A=\frac{\sin^2\theta}{\cos^2\theta}\times\frac{1}{\sin^2\theta}$$ $$A=\frac{1}{\cos^2\theta}$$ This is the result needed to find.
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.