Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.1 Fundamental Identities - 5.1 Exercises - Page 201: 50


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

Work Step by Step

Pythagorean Identities: $$\cot^2 x+1=\csc^2 x$$ Therefore, $$\cot^2 x=\csc^2 x-1$$ We now take the square root of both sides to get $\cot x$ $$\sqrt{\cot^2 x}=\sqrt{\csc^2 x-1}$$ $$\cot x=\pm\sqrt{\csc^2 x-1}$$ (Do not forget the $\pm$ sign, as $\cot x$ might be positive or negative)
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