Answer
$sin~φ(csc~φ-sin~φ)=cos^2φ$
Work Step by Step
We know that:
$csc~φ=\frac{1}{sin~φ}$
$sin^2φ+cos^2φ=1$
$cos^2φ=1-sin^2φ$
So:
$sin~φ(csc~φ-sin~φ)=sin~φ(\frac{1}{sin~φ}-sin~φ)=1-sin^2φ=cos^2φ$
Algebra and Trigonometry 10th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
9781337271172
ISBN 13:
978-1-33727-117-2
Chapter 7 - 7.1 - Using Fundamental Identities - 7.1 Exercises - Page 513: 35
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