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 5.1 Fundamental Identities - 5.1 Exercises - Page 201: 59



Work Step by Step

$$A=\sin^2\theta(\csc^2\theta-1)$$ - Pythagorean Identity: $$\cot^2\theta+1=\csc^2\theta$$ Replace into $A$: $$A=\sin^2\theta(\cot^2\theta+1-1)$$ $$A=\sin^2\theta(\cot^2\theta)$$ - Quotient Identity: $$\cot\theta=\frac{\cos\theta}{\sin\theta}$$ Replace into $A$: $$A=\sin^2\theta\times\frac{\cos^2\theta}{\sin^2\theta}$$ $$A=\cos^2\theta$$
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.