Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 14 - Trigonometric Identities and Equations - 14-1 Trigonometric Identities - Practice and Problem-Solving Exercises: 20

Answer

$$\csc^{2}\theta$$

Work Step by Step

Use the Reciprocal Identity: $$\sec\theta=\frac{1}{\cos\theta}$$ and the Cotangent Identity: $$\cot\theta=\frac{\cos\theta}{\sin\theta}$$ To obtain: $$\sec^{2}\theta\cot^{2}\theta=\bigg(\frac{1}{\cos^{2}\theta}\bigg)\bigg(\frac{\cos^{2}\theta}{\sin^{2}\theta}\bigg)=\frac{1}{\sin^{2}\theta}$$ Use the Reciprocal Identity: $$\csc\theta=\frac{1}{\sin\theta}$$ To obtain: $$\sec^{2}\theta\cot^{2}\theta=\csc^{2}\theta$$
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