Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.2 - Verifying Trigonometric Identities - 7.2 Exercises - Page 521: 53


Identity is verified. $cos^3~x~sin^2x=(sin^2x-sin^4x)cos~x$

Work Step by Step

We know that: $sin^2x+cos^2x=1$ $cos^2x=1-sin^2x$ Start at the right side of the equation: $(sin^2x-sin^4x)cos~x=sin^2x(1-sin^2x)cos~x=sin^2x(cos^2x)cos~x=sin^2x~cos^3~x$
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