Answer
See below.
Work Step by Step
$RHS=\frac{(sin\theta+cos\theta)(sin^2\theta-sin\theta cos\theta+cos^2\theta)}{sin\theta+cos\theta}=sin^2\theta+cos^2\theta-sin\theta cos\theta=1-\frac{1}{2}sin(2\theta)=LHS$
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 7 - Analytic Trigonometry - 7.6 Double-angle and Half-angle Formulas - 7.6 Assess Your Understanding - Page 498: 64
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