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: 54


Identity is verified. $sin^4x+cos^4x=1-2~cos^2x+2~cos^4x$

Work Step by Step

We know that: $sin^2x+cos^2x=1$ $sin^2x=1-cos^2x$ Start at the left side of the equation: $sin^4x+cos^4x=(sin^2x)^2+cos^4x=(1-cos^2x)^2+cos^4x=1-2~cos^2x+(cos^2x)^2+cos^4x=1-2~cos^2x+cos^4x+cos^4x=1-2~cos^2x+2~cos^4x$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.