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 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 208: 15



Work Step by Step

$$A=\frac{1}{\csc^2\theta}+\frac{1}{\sec^2\theta}$$ $$A=\Bigg(\frac{1}{\csc\theta}\Bigg)^2+\Bigg(\frac{1}{\sec\theta}\Bigg)^2$$ - Reciprocal Identities: $$\csc\theta=\frac{1}{\sin\theta}\hspace{2cm}\sec\theta=\frac{1}{\cos\theta}$$ Therefore, $$\frac{1}{\csc\theta}=\sin\theta\hspace{2cm}\frac{1}{\sec\theta}=\cos\theta$$ $$A=\sin^2\theta+\cos^2\theta$$ $$A=1$$ (Pythagorean Identity)
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