Short Answer

Establish each identity.
$\frac{\sin θ + \cos θ}{\sin θ} - \frac{\cos θ - \sin θ}{\cos θ} = s e c θ c s c θ$

The left side of the given equation has been simplified to bring 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 $\frac{\sin θ + \cos θ}{\sin θ} - \frac{\cos θ - \sin θ}{\cos θ} = s e c θ c s c θ$

Step 2. Calculation

Consider the left side of the given equation and simplify to bring the right side in order to establish the equation.

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

Hence, Proved

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Precalculus Enhanced with Graphing Utilities

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Short Answer

Establish each identity.
$\frac{\sin θ + \cos θ}{\sin θ} - \frac{\cos θ - \sin θ}{\cos θ} = s e c θ c s c θ$

Step by Step Solution

Step 1. Given Information

Step 2. Calculation

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Short Answer

Establish each identity. sinθ+cosθsinθ-cosθ-sinθcosθ=secθcscθ

Step by Step Solution

Step 1. Given Information

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Establish each identity.
$\frac{\sin θ + \cos θ}{\sin θ} - \frac{\cos θ - \sin θ}{\cos θ} = s e c θ c s c θ$