Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 14 - Trigonometric Identities and Equations - 14-1 Trigonometric Identities - Lesson Check - Page 908: 4



Work Step by Step

Step 1: By definition, $\tan\theta =\frac{\sin\theta}{\cos\theta}$ and $\cot\theta=\frac{\cos\theta}{\sin\theta}$ Hence, $\tan\theta\times \cot\theta-\sin^{2}\theta= \frac{\sin\theta}{\cos\theta}\times\frac{\cos\theta}{\sin\theta}-\sin^{2}\theta$ Step 2: Simplifying the expression gives, $\tan\theta\times \cot\theta-\sin^{2}\theta= 1-\sin^{2}\theta$ Step 3: By the identity $\sin^{2}\theta+\cos^{2}\theta=1$, replace $1-\sin^{2}\theta$ by $\cos^{2}\theta$ Hence, $\tan\theta\times \cot\theta-\sin^{2}\theta = \cos^{2}\theta$
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