Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - Chapter Test - Page 554: 18


$\dfrac{-\sqrt 6+\sqrt 2}{4}$

Work Step by Step

By using the Sum and Difference formulas: $\cos (a+b)=\cos a \cos b -\sin a \sin b$ and $\cos (a-b)=\cos a \cos b +\sin a \sin b$ $\cos 105^{\circ}=\cos (135^{\circ}-30^{\circ})$ or, $=\cos 135^{\circ} \cos 30^{\circ} +\sin 135^{\circ} \sin 30^{\circ}$ or, $=(\dfrac{-\sqrt 2}{2})(\dfrac{\sqrt 3}{2})+(\dfrac{\sqrt 2}{2})(\dfrac{1}{2})$ or, $=\dfrac{-\sqrt 6+\sqrt 2}{4}$
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