Answer
$cos~x-csc~x~cot~x=-cos~x~cot^2x$
Work Step by Step
$cot^2x+1=csc^2x$
$1-csc^2x=-cot^2x$
$cos~x-csc~x~cot~x=cos~x-\frac{1}{sin~x}\frac{cos~x}{sin~x}=cos~x(1-\frac{1}{sin^2x})=cos~x(1-csc^2x)=cos~x(-cot^2x)=-cos~x~cot^2x$
Algebra and Trigonometry 10th Edition
by Larson, Ron
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: 61
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