Answer
See below.
Work Step by Step
$RHS=\frac{sin^3\theta+cos^3\theta}{sin\theta+cos\theta}
=\frac{(sin\theta+cos\theta)(sin^2\theta+cos^2\theta-sin\theta cos\theta)}{sin\theta+cos\theta}
=1-sin\theta cos\theta=1-\frac{1}{2}sin(2\theta)=LHS$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 6 - Analytic Trigonometry - Section 6.6 Double-angle and Half-angle Formulas - 6.6 Assess Your Understanding - Page 519: 62
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