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: 68



Work Step by Step

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