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Q. 71

Expert-verified

Precalculus Enhanced with Graphing Utilities

Found in: Page 475

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Establish each identity.
$s e c θ - \cos θ = \sin θ \tan θ$

The left side of the given equation has been simplified to give the right side.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

The given equation is $s e c θ - \cos θ = \sin θ \tan θ$

Step 2. Calculation

Consider the left side of the given equation and simplify.

$s e c θ - \cos θ = \frac{1}{\cos θ} - \cos θ = \frac{1 - \cos^{2} θ}{\cos θ} = \frac{\sin^{2} θ}{\cos θ} = \sin θ \frac{\sin θ}{\cos θ} = \sin θ \tan θ$

Thus, the given identity is established.

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