Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.1 Fundamental Identities - 7.1 Exercises: 66

Answer

$\cos ^{2}\theta \sin ^{2}\theta $

Work Step by Step

$\dfrac {1-\sin ^{2}\left( -\theta \right) }{1+\cot ^{2}\left( -\theta \right) }=\dfrac {1-\left( \sin \left( -\theta \right) \right) ^{2}}{1+\dfrac {\cos ^{2}\left( -\theta \right) }{\sin ^{2}\left( -\theta \right) }}=\dfrac {1-\left( -\sin \theta \right) ^{2}}{1+\dfrac {\cos ^{2}\theta }{\left( -\sin \theta \right) ^{2}}}=\dfrac {\cos ^{2}\theta }{1+\dfrac {\cos ^{2}\theta }{\sin ^{2}\theta }}=\dfrac {\cos ^{2}\theta \sin ^{2}\theta }{\cos ^{2}\theta +\sin ^{2}\theta }=\cos ^{2}\theta \sin ^{2}\theta $
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