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: 67



Work Step by Step

$$A=\sec\theta-\cos\theta$$ - Reciprocal Identities: $$\sec\theta=\frac{1}{\cos\theta}$$ Replace into $A$: $$A=\frac{1}{\cos\theta}-\cos\theta$$ $$A=\frac{1-\cos^2\theta}{\cos\theta}$$ - Pythagorean Identities: $$\sin^2\theta=1-\cos^2\theta$$ Replace into $A$: $$A=\frac{\sin^2\theta}{\cos\theta}$$ $$A=\frac{\sin\theta}{\cos\theta}\times\sin\theta$$ - Quotient Identities: $$\tan\theta=\frac{\sin\theta}{\cos\theta}$$ Replace into $A$: $$A=\tan\theta\sin\theta$$
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