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 Equations - 7.4 Exercises - Page 539: 63


The identity is verified. $cos(\pi-θ)+sin(\frac{\pi}{2}-θ)=0$

Work Step by Step

$cos(u-v)=cos~u~cos~v+sin~u~sin~v$ $sin(u+v)=sin~u~cos~v+cos~u~sin~v$ $cos(\pi-θ)+sin(\frac{\pi}{2}-θ)=cos~\pi~cos~θ+sin~\pi~sin~θ+sin~\frac{\pi}{2}~cos~θ+cos~\frac{\pi}{2}~sin~θ=(-1)cos~θ+0~sin~θ+1~cos~θ+0~sin~θ=-cos~θ+cos~θ=0$
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