Trigonometry (10th Edition)

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

Chapter 5 - Trigonometric Identities - Section 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 202: 37

Answer

$$\frac{1-\sin^2\beta}{\cos\beta}=\cos\beta$$ We simplify the left side, using Pythagorean Identity for the numerator.

Work Step by Step

$$\frac{1-\sin^2\beta}{\cos\beta}=\cos\beta$$ The left side is more complex, so we would simplify it first. $$A=\frac{1-\sin^2\beta}{\cos\beta}$$ According to a Pythagorean Identity, $$1-\sin^2\beta=\cos^2\beta$$ $A$ would become $$A=\frac{\cos^2\beta}{\cos\beta}$$ $$A=\cos\beta$$ The left side has been simplified to the right side. It is thus an identity.
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