Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.2 Verifying Trigonometric Identities - 7.2 Exercises - Page 666: 30


$=\left( \cot ^{2}x+1\right) \left( \cot ^{2}x+2\right) $

Work Step by Step

$\cot ^{4}x+3\cot ^{2}x+2=\cot ^{4}x+2\cot ^{2}x+1+\left( 1+\cot ^{2}x\right) =\left( \cot ^{2}x+1\right) ^{2}+\left( \cot ^{2}x+1\right) =\left( \cot ^{2}x+1\right) \left( \cot ^{2}x+1+1\right) $ $=\left( \cot ^{2}x+1\right) \left( \cot ^{2}x+2\right) $
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