Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 208: 29


$$\cos^4x+2\cos^2x+1=(\cos^2 x+1)^2$$

Work Step by Step

$$A=\cos^4x+2\cos^2x+1$$ To make the matter easier, we would take $u=\cos^2 x$, which means $u^2=(\cos^2 x)^2=\cos^4 x$. Therefore, $$A=u^2+2u+1$$ So now we can see that this is a form of $(a+b)^2=a^2+2ab+b^2$ with $a=u$ and $b=1$. That shows, $$A=(u+1)^2$$ Eventually, $$A=(\cos^2 x+1)^2$$
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.