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: 44


$$1-\frac{1}{\sec^2x}=\sin^2 x$$

Work Step by Step

$$A=1-\frac{1}{\sec^2x}$$ $$A=1-\Big(\frac{1}{\sec x}\Big)^2$$ From Reciprocal Identities: $$\sec x=\frac{1}{\cos x}$$ therefore, $$\cos x=\frac{1}{\sec x}$$ so, $$\cos^2x=\Big(\frac{1}{\sec x}\Big)^2$$ That makes $A$ into $$A=1-\cos^2 x$$ $$A=\sin^2x\hspace{1cm}\text{(Pythagorean Identity)}$$
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