Answer
See below.
Work Step by Step
$LHS=(sin\alpha-cos\beta)^2+(cos\beta+sin\alpha)(cos\beta-sin\alpha)
=sin^2\alpha+cos^2\beta-2sin\alpha cos\beta+cos^2\beta-sin^2\alpha
=-2cos\beta(sin\alpha-cos\beta)=RHS$
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 6.4 Trigonometric Identities - 6.4 Assess Your Understanding - Page 498: 96
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