Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - Summary Exercises Verifying Trigonometric Identities - Exercises - Page 696: 22


$\dfrac {\tan \theta -\cot \theta }{\tan \theta +\cot \theta }=2\sin ^{2}\theta -1$

Work Step by Step

$\dfrac {\tan \theta -\cot \theta }{\tan \theta +\cot \theta }=\dfrac {\dfrac {\sin \theta }{\cos \theta }-\dfrac {\cos \theta }{\sin \theta }}{\dfrac {\sin \theta }{\cos a}+\dfrac {\cos \theta }{\sin \theta }}=\dfrac {\dfrac {\sin ^{2}\theta -\cos ^{2}\theta }{\cos \theta \sin \theta }}{\dfrac {\sin ^{2}\theta +\cos ^{2}\theta }{\cos \theta \sin \theta }}=\sin ^{2}\theta -\cos ^{2}\theta =\sin ^{2}\theta -\left( 1-\sin ^{2}\theta \right) =2\sin ^{2}\theta -1$
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