Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises - Page 694: 70


$\cot 82.5=\tan7.5$

Work Step by Step

$\sqrt {\dfrac {1+\cos 165}{1-\cos 165}} =\sqrt {\dfrac {1+\cos \left( 2\times \dfrac {165}{2}\right) }{1-\cos \left( 2\times \dfrac {165}{2}\right) }}=\sqrt {\dfrac {1+\left( \cos ^{2}\dfrac {165}{2}-\sin ^{2}\dfrac {165}{2}\right) }{1-\left( \cos ^{2}\dfrac {165}{2}-\sin ^{2}\dfrac {165}{2}\right) }}=\sqrt {\dfrac {2\cos ^{2}\dfrac {165}{2}}{2\sin ^{2}\dfrac {165}{2}}}=\cot \dfrac {165}{2}=\cot 82.5=\tan7.5$
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