Answer
$-cos~\frac{4\pi}{5}$
Work Step by Step
We can use this identity: $cos~2x = cos^2~x - sin^2~x$
$sin^2~\frac{2\pi}{5}-cos^2~\frac{2\pi}{5}$
$= -(cos^2~\frac{2\pi}{5}-sin^2~\frac{2\pi}{5})$
$= -cos~\frac{4\pi}{5}$
Trigonometry (11th Edition) Clone
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
978-0-13-421743-7
ISBN 13:
978-0-13421-743-7
Chapter 5 - Trigonometric Identities - Section 5.5 Double-Angle Identities - 5.5 Exercises - Page 237: 47
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