Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 99 (page 487)

Show that $\tan^{- 1} (\frac{1}{v}) = \frac{蟺}{2} - \tan^{- 1} v$ , if $v > 0$

Short Answer

Expert verified

The equation $\tan^{- 1} (\frac{1}{v}) = \frac{蟺}{2} - \tan^{- 1} v$ can be obtained by the formula

$\tan^{- 1} v + c o t^{- 1} v = \frac{蟺}{2} c o t^{- 1} v = \frac{蟺}{2} - \tan^{- 1} v \tan^{- 1} v + c o t^{- 1} v = \frac{蟺}{2} \tan^{- 1} (\frac{1}{v}) = \frac{蟺}{2} - \tan^{- 1} v$

Step by step solution

Step 1. Given data

The given equation for verification is

$\tan^{- 1} (\frac{1}{v}) = \frac{蟺}{2} - \tan^{- 1} v$

Step 2. Consider

Consider

$c o t^{- 1} v = A v = c o t A \frac{1}{v} = \frac{1}{c o t A} \frac{1}{v} = \tan A \tan^{- 1} (\frac{1}{v}) = A \tan^{- 1} (\frac{1}{v}) = c o t^{- 1} v 鈰� (1)$

Step 3. proof

Use formula

$\tan^{- 1} v + c o t^{- 1} v = \frac{蟺}{2} c o t^{- 1} v = \frac{蟺}{2} - \tan^{- 1} v$

From equation $1$

$c o t^{- 1} v = \frac{蟺}{2} - \tan^{- 1} v \tan^{- 1} (\frac{1}{v}) = \frac{蟺}{2} - \tan^{- 1} v$

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Show that $\tan^{- 1} (\frac{1}{v}) = \frac{蟺}{2} - \tan^{- 1} v$ , if $v > 0$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Consider

Step 3. proof

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

91影视

Show thattan-11v=蟺2-tan-1v, ifv>0

Short Answer

Step by step solution

Step 1. Given data

Step 2. Consider

Step 3. proof

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Show that $\tan^{- 1} (\frac{1}{v}) = \frac{蟺}{2} - \tan^{- 1} v$ , if $v > 0$