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 - Practice and Problem-Solving Exercises: 45

Answer

$$cot\theta=\pm\sqrt{csc^{2}\theta-1}$$

Work Step by Step

By identity, $csc^{2}\theta=1+cot^{2}\theta$. Subtracting 1 from both sides $csc^{2}{\theta}-1=\cot^{2}{\theta} \\\cot^{2}{\theta}=\csc^{2}{\theta}-1$ Taking square-root on both sides, $$\cot\theta=\pm\sqrt{\csc^{2}\theta-1}$$
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