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: 73

Answer

$\tan ^{2}\theta $

Work Step by Step

$\dfrac {1+\tan ^{2}\theta }{1+\cot ^{2}\theta }=\dfrac {1+\dfrac {\sin ^{2}\theta }{\cos ^{2}\theta }}{1+\dfrac {\cos ^{2}\theta }{\sin ^{2}\theta }}=\dfrac {\dfrac {\cos ^{2}\theta +\sin ^{2}\theta }{\cos ^{2}\theta }}{\dfrac {\sin ^{2}\theta +\cos ^{2}\theta }{\sin ^{2}\theta }}=\dfrac {\sin ^{2}\theta }{\cos ^{2}\theta }=\tan ^{2}\theta $
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