Chapter 7: Q. 49 (page 474)

In problems 19-98, establish each identity.
$\frac{1 - \sin (v)}{\cos (v)} + \frac{\cos (v)}{1 - \sin (v)} = 2 \sec (v)$

Short Answer

Expert verified

We have proved the identity $\frac{1 - \sin (v)}{\cos (v)} + \frac{\cos (v)}{1 - \sin (v)} = 2 \sec (v)$ .

Step by step solution

Step 1. Given information.

We have:

$\frac{1 - \sin (v)}{\cos (v)} + \frac{\cos (v)}{1 - \sin (v)} = 2 \sec (v)$

Step 2. Establish the identity.

Take the left hand side:

$\frac{1 - \sin (v)}{\cos (v)} + \frac{\cos (v)}{1 - \sin (v)}$

$= \frac{{(1 - \sin (v))}^{2} + \cos^{2} (v)}{(1 - \sin (v)) \cos (v)} = \frac{1 + \sin^{2} (v) - 2 \sin (v) + \cos^{2} (v)}{(1 - \sin (v)) \cos (v)} = \frac{2 - 2 \sin (v)}{(1 - \sin (v)) \cos (v)} = \frac{2 (1 - \sin (v))}{(1 - \sin (v)) \cos (v)} = \frac{2}{\cos (v)} = 2 \sec (v)$

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.

In problems 19-98, establish each identity.
$\frac{1 - \sin (v)}{\cos (v)} + \frac{\cos (v)}{1 - \sin (v)} = 2 \sec (v)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Establish the identity.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Pure Maths

Decision Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In problems 19-98, establish each identity. 1-sinvcosv+cosv1-sinv=2secv

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Establish the identity.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Pure Maths

Decision Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In problems 19-98, establish each identity.
$\frac{1 - \sin (v)}{\cos (v)} + \frac{\cos (v)}{1 - \sin (v)} = 2 \sec (v)$