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: 3


$\tan \dfrac {x}{2}=cscx-\cot x $

Work Step by Step

$\tan \dfrac {x}{2}=\dfrac {\sin \dfrac {x}{2}}{\cos \dfrac {x}{2}}=\dfrac {\sqrt {\dfrac {1-\cos x}{2}}}{\sqrt {\dfrac {1+\cos x}{2}}}=\sqrt {\dfrac {1-\cos x}{1+\cos x}}=\sqrt {\dfrac {\left( 1-\cos x\right) \left( 1-\cos x\right) }{\left( 1+\cos x\right) \left( 1-\cos x\right) }}=\sqrt {\dfrac {\left( 1-\cos x\right) ^{2}}{\sin ^{2}x}}=\dfrac {1-\cos x}{\sin x}=cscx-\cot x $
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