Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - 7.1 Fundamental Identities - 7.1 Exercises: 46

Answer

$\pm \dfrac {2\sqrt {2\left( x+2\right) }}{x}$

Work Step by Step

$\tan \theta =\dfrac {\sin \theta }{\cos \theta }=\pm \dfrac {\sqrt {1-\cos ^{2}\theta }}{\cos \theta }=\pm \sqrt {\dfrac {1}{\cos ^{2}\theta }-1}=\pm \sqrt {sec^2\theta -1}$$=\pm \sqrt {\left( \dfrac {x+4}{x}\right) ^{2}-1}=\pm \sqrt {\dfrac {\left( x+4\right) ^{2}-x^{2}}{x^{2}}}=\pm \dfrac {\sqrt {\left( x+4-x\right) \left( x+4+x\right) }}{x}=\pm \dfrac {2\sqrt {2\left( x+2\right) }}{x}$
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