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: 62



Work Step by Step

$$A=(\sec\theta-1)(\sec\theta+1)$$ As $(a-b)(a+b)=a^2-b^2$: $$A=\sec^2\theta-1$$ - Reciprocal Identity: $$\sec\theta=\frac{1}{\cos\theta}$$ Replace into $A$: $$A=\frac{1}{\cos^2\theta}-1$$ $$A=\frac{1-\cos^2\theta}{\cos^2\theta}$$ - Pythagorean Identity: $$\sin^2\theta=1-\cos^2\theta$$ Replace into $A$: $$A=\frac{\sin^2\theta}{\cos^2\theta}=\Bigg(\frac{\sin\theta}{\cos\theta}\Bigg)^2$$ - Quotient Identity: $$\tan\theta=\frac{\sin\theta}{\cos\theta}$$ Replace into $A$: $$A=\tan^2\theta$$
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