Algebra and Trigonometry 10th Edition

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

Chapter 7 - Review Exercises - Page 553: 67


The identity is verified. $(sin~x+cos~x)^2=1+sin~2x$

Work Step by Step

Use: $cos^2x+sin^2x=1$ and $sin~2x=2~sin~x~cos~x$ Start on the left side: $(sin~x+cos~x)^2=sin^2x+2~sin~x~cos~x+cos^2x=(sin^2x+cos^2x)+2~sin~x~cos~x=1+sin~2x$
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