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: 33

Answer

$$\csc\theta$$

Work Step by Step

Simplify $$\sin\theta(1+\cot^{2}\theta).$$ Use the Reciprocal Identity $$\sin\theta=\frac{1}{\csc\theta}$$ and the Pythagorean Identity $$1+\cot^{2}\theta=\csc^{2}\theta$$ to obtain $$\sin\theta(1+\cot^{2}\theta)=\bigg(\frac{1}{\csc\theta}\bigg)\csc^{2}\theta=\csc\theta.$$
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