Algebra and Trigonometry 10th Edition

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

Chapter 7 - 7.4 - Sum and Difference Formulas - 7.4 Exercises - Page 538: 9


(a) $sin(135°-30°)=\frac{\sqrt 6-\sqrt 2}{4}$ (b) $sin~135°-cos~30°=-\frac{\sqrt 3-\sqrt 2}{2}$

Work Step by Step

(a) $sin(135°-30°)=sin~135°cos~~30°-cos~135°sin~30°=\frac{\sqrt 2}{2}\frac{\sqrt 3}{2}-(\frac{\sqrt 2}{2})\frac{1}{2}=\frac{\sqrt 6}{4}-\frac{\sqrt 2}{4}=\frac{\sqrt 6-\sqrt 2}{4}$ (b) $sin~135°-cos~30°=\frac{\sqrt 2}{2}-\frac{\sqrt 3}{2}=\frac{\sqrt 2-\sqrt 3}{2}=-\frac{\sqrt 3-\sqrt 2}{2}$
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