Trigonometry (10th Edition)

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

Chapter 5 - Trigonometric Identities - Section 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 202: 20

Answer

$$\cot^4x+3\cot^2x+2=(\cot^2x+1)(\cot^2x+2)$$

Work Step by Step

$$A=\cot^4x+3\cot^2x+2$$ We would rewrite $3\cot^2 x$ into $(\cot^2 x+2\cot^2 x)$. $$A=\cot^4 x+\cot^2x+2\cot^2x+2$$ $$A=\cot^2x(\cot^2x+1)+2(\cot^2x+1)$$ $$A=(\cot^2x+1)(\cot^2x+2)$$
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