Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - 7.2 Verifying Trigonometric Identities - 7.2 Exercises - Page 667: 70


$\dfrac {\cot ^{2}t-1}{1+\cot ^{2}t}=1-\sin ^{2}t-\sin ^{2}t=1-2\sin ^{2}t$

Work Step by Step

$\dfrac {\cot ^{2}t-1}{1+\cot ^{2}t}=\dfrac {\dfrac {\cos ^{2}t}{\sin ^{2}t}-1}{1+\dfrac {\cos ^{2}t}{\sin ^{2}t}}=\dfrac {\cos ^{2}t-\sin ^{2}t}{\cos ^{2}t+\sin ^{2}t}=\cos ^{2}t-\sin ^{2}t=1-\sin ^{2}t-\sin ^{2}t=1-2\sin ^{2}t$
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