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: 60



Work Step by Step

$$A=\cot^2\theta(1+\tan^2\theta)$$ - Pythagorean Identity: $$\tan^2\theta+1=\sec^2\theta$$ Replace into $A$: $$A=\cot^2\theta\times\sec^2\theta$$ - Quotient Identity: $$\cot\theta=\frac{\cos\theta}{\sin\theta}$$ - Reciprocal Identity: $$\sec\theta=\frac{1}{\cos\theta}$$ Replace them into $A$: $$A=\frac{\cos^2\theta}{\sin^2\theta}\times\frac{1}{\cos^2\theta}$$ $$A=\frac{1}{\sin^2\theta}=\Big(\frac{1}{\sin\theta}\Big)^2$$ $$A=\csc^2\theta\hspace{1cm}\text{(Reciprocal Identity)}$$
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