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 520: 14


The trigonometric Identity is verified. $sin^2α-sin^4α=cos^2α-cos^4α$

Work Step by Step

We know that: $cos^2α+sin^2α=1$ $sin^2α=1-cos^2α$ Start al the left side of the equation: $sin^2α-sin^4α=sin^2α-(sin^2α)^2=1-cos^2α-(1-cos^2α)^2=1-cos^2α-(1-2~cos^2α+cos^4α)=1-cos^2α-1+2~cos^2α-cos^4α=cos^2α-cos^4α$
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