Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 5 - Trigonometric Identities - Section 5.1 Fundamental Identities - 5.1 Exercises - Page 196: 78

Answer

$$\cos\theta(\cos\theta-\sec\theta)=-\sin^2\theta$$

Work Step by Step

$$A=\cos\theta(\cos\theta-\sec\theta)$$ - Reciprocal Identity: $$\sec\theta=\frac{1}{\cos\theta}$$ Replace into $A$: $$A=\cos\theta(\cos\theta-\frac{1}{\cos\theta})$$ $$A=\cos^2\theta-\cos\theta\times\frac{1}{\cos\theta}$$ $$A=\cos^2\theta-1$$ $$A=-(1-\cos^2\theta)$$ - Pythagorean Identity: $$\sin^2\theta=1-\cos^2\theta$$ Replace into $A$: $$A=-\sin^2\theta$$
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