Chapter 7: Q. 80 (page 475)

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

Short Answer

Expert verified

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

Step by step solution

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Pure Maths

Calculus

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Pure Maths

Calculus

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

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