Trigonometry (11th Edition) Clone

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

Chapter 5 - Review Exercises - Page 249: 56


$\frac{2~cot~x}{tan~2x} = csc^2~x-2$

Work Step by Step

$\frac{2~cot~x}{tan~2x} = \frac{2~cos~x~cos~2x}{sin~x~sin~2x}$ $\frac{2~cot~x}{tan~2x} = \frac{2~cos~x~(cos^2~x-sin^2~x)}{sin~x~2~sin~x~cos~x}$ $\frac{2~cot~x}{tan~2x} = \frac{cos^2~x-sin^2~x}{sin^2~x}$ $\frac{2~cot~x}{tan~2x} = \frac{(1-sin^2~x)-sin^2~x}{sin^2~x}$ $\frac{2~cot~x}{tan~2x} = \frac{1-2~sin^2~x}{sin^2~x}$ $\frac{2~cot~x}{tan~2x} = \frac{1}{sin^2~x}-\frac{2~sin^2~x}{sin^2~x}$ $\frac{2~cot~x}{tan~2x} = csc^2~x-2$
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