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: 18



Work Step by Step

$\left( \tan x+\cot x\right) ^{2}=\tan ^{2}x+\cot ^{2}x+2\tan x\cot x=\tan ^{2}x+\cot ^{2}x+2$ $=\tan ^{2}x+1+\cot ^{2}x+1=\dfrac {1}{\cos ^{2}x}+\dfrac {1}{\sin ^{2}x}=\dfrac {\cos ^{2}x+\sin ^{2}x}{\cos ^{2}x\sin ^{2}x}=\dfrac {1}{\cos ^{2}x\sin ^{2}x}=sec^{2}xcsc^{2}x$
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