Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 13.9, Problem 30WE
To determine

To Find: The Equation in terms of cotα and cotβ .

Expert Solution & Answer
Check Mark

Answer to Problem 30WE

The Equation in terms of cotα and cotβ is cot(α−β)=cotαcotβ+1cotβ−cotα .

Explanation of Solution

Given information:

The given equation is cot(α−β) .

Calculation:

Consider the formulas:

Addition formulas for the tangent,

  tan(α−β)=tanα−tanβ1+tanαtanβtan(α+β)=tanα+tanβ1−tanαtanβ

Applying reciprocal identity, we get

  cot(α−β)=1tan(α−β)

Applying addition formulas for the tangent, we get

  cot(α−β)=1tanα−tanβ1+tanαtanβ=1+tanαtanβtanα−tanβ

Applying reciprocal identity, we get

  cot(α−β)=1+1cotα1cotβ1cotα−1cotβ=cotαcotβ+1cotβ−cotα

Therefore, expressing cot(α−β) in terms of cotα and cotβ , we get,

  cot(α−β)=cotαcotβ+1cotβ−cotα .

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Chapter 13.9, Problem 31WE

Chapter 13 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 13.1 - Prob. 1OECh. 13.1 - Prob. 2OECh. 13.1 - Prob. 3OECh. 13.1 - Prob. 4OECh. 13.1 - Prob. 5OECh. 13.1 - Prob. 6OECh. 13.1 - Prob. 7OECh. 13.1 - Prob. 8OECh. 13.1 - Prob. 9OECh. 13.1 - Prob. 10OE
Ch. 13.1 - Prob. 11OECh. 13.1 - Prob. 12OECh. 13.1 - Prob. 13OECh. 13.1 - Prob. 1WECh. 13.1 - Prob. 2WECh. 13.1 - Prob. 3WECh. 13.1 - Prob. 4WECh. 13.1 - Prob. 5WECh. 13.1 - Prob. 6WECh. 13.1 - Prob. 7WECh. 13.1 - Prob. 8WECh. 13.1 - Prob. 9WECh. 13.1 - Prob. 10WECh. 13.1 - Prob. 11WECh. 13.1 - Prob. 12WECh. 13.1 - Prob. 13WECh. 13.1 - Prob. 14WECh. 13.1 - Prob. 15WECh. 13.1 - Prob. 16WECh. 13.1 - Prob. 17WECh. 13.1 - Prob. 18WECh. 13.1 - Prob. 19WECh. 13.1 - Prob. 20WECh. 13.1 - Prob. 21WECh. 13.1 - Prob. 22WECh. 13.1 - Prob. 23WECh. 13.1 - Prob. 24WECh. 13.1 - Prob. 25WECh. 13.1 - Prob. 26WECh. 13.1 - Prob. 27WECh. 13.1 - Prob. 28WECh. 13.1 - Prob. 29WECh. 13.1 - Prob. 30WECh. 13.1 - Prob. 31WECh. 13.1 - Prob. 32WECh. 13.1 - Prob. 33WECh. 13.1 - Prob. 34WECh. 13.1 - Prob. 35WECh. 13.1 - Prob. 36WECh. 13.1 - Prob. 37WECh. 13.1 - Prob. 38WECh. 13.1 - Prob. 39WECh. 13.1 - Prob. 40WECh. 13.1 - Prob. 41WECh. 13.1 - Prob. 42WECh. 13.1 - Prob. 43WECh. 13.1 - Prob. 44WECh. 13.1 - Prob. 45WECh. 13.1 - Prob. 46WECh. 13.1 - Prob. 47WECh. 13.1 - Prob. 48WECh. 13.1 - Prob. 49WECh. 13.1 - Prob. 50WECh. 13.1 - Prob. 51WECh. 13.1 - Prob. 52WECh. 13.1 - Prob. 53WECh. 13.1 - Prob. 54WECh. 13.1 - Prob. 55WECh. 13.1 - Prob. 56WECh. 13.1 - Prob. 57WECh. 13.1 - Prob. 58WECh. 13.1 - Prob. 59WECh. 13.1 - Prob. 60WECh. 13.1 - Prob. 1PCh. 13.1 - Prob. 2PCh. 13.1 - Prob. 3PCh. 13.1 - Prob. 4PCh. 13.1 - Prob. 5PCh. 13.1 - Prob. 6PCh. 13.1 - Prob. 7PCh. 13.1 - Prob. 8PCh. 13.1 - Prob. 9PCh. 13.1 - Prob. 10PCh. 13.1 - Prob. 11PCh. 13.1 - Prob. 12PCh. 13.1 - Prob. 13PCh. 13.1 - Prob. 1MRECh. 13.1 - Prob. 2MRECh. 13.1 - Prob. 3MRECh. 13.1 - Prob. 4MRECh. 13.1 - Prob. 5MRECh. 13.1 - Prob. 6MRECh. 13.1 - Prob. 7MRECh. 13.1 - Prob. 8MRECh. 13.2 - Prob. 1OECh. 13.2 - Prob. 2OECh. 13.2 - Prob. 3OECh. 13.2 - Prob. 4OECh. 13.2 - Prob. 5OECh. 13.2 - Prob. 6OECh. 13.2 - Prob. 7OECh. 13.2 - Prob. 8OECh. 13.2 - Prob. 9OECh. 13.2 - Prob. 10OECh. 13.2 - Prob. 11OECh. 13.2 - Prob. 12OECh. 13.2 - Prob. 13OECh. 13.2 - Prob. 14OECh. 13.2 - Prob. 15OECh. 13.2 - Prob. 16OECh. 13.2 - Prob. 17OECh. 13.2 - Prob. 18OECh. 13.2 - Prob. 1WECh. 13.2 - Prob. 2WECh. 13.2 - Prob. 3WECh. 13.2 - Prob. 4WECh. 13.2 - Prob. 5WECh. 13.2 - Prob. 6WECh. 13.2 - Prob. 7WECh. 13.2 - Prob. 8WECh. 13.2 - Prob. 9WECh. 13.2 - Prob. 10WECh. 13.2 - Prob. 11WECh. 13.2 - Prob. 12WECh. 13.2 - Prob. 13WECh. 13.2 - Prob. 14WECh. 13.2 - Prob. 15WECh. 13.2 - Prob. 16WECh. 13.2 - Prob. 17WECh. 13.2 - Prob. 18WECh. 13.2 - Prob. 19WECh. 13.2 - Prob. 20WECh. 13.2 - Prob. 21WECh. 13.2 - Prob. 22WECh. 13.2 - Prob. 23WECh. 13.2 - Prob. 24WECh. 13.2 - Prob. 25WECh. 13.2 - Prob. 26WECh. 13.2 - Prob. 27WECh. 13.2 - Prob. 28WECh. 13.2 - Prob. 29WECh. 13.2 - Prob. 30WECh. 13.2 - Prob. 31WECh. 13.2 - Prob. 32WECh. 13.3 - Prob. 1OECh. 13.3 - Prob. 2OECh. 13.3 - Prob. 3OECh. 13.3 - Prob. 4OECh. 13.3 - Prob. 5OECh. 13.3 - Prob. 6OECh. 13.3 - Prob. 7OECh. 13.3 - Prob. 8OECh. 13.3 - Prob. 9OECh. 13.3 - Prob. 1WECh. 13.3 - Prob. 2WECh. 13.3 - Prob. 3WECh. 13.3 - Prob. 4WECh. 13.3 - Prob. 5WECh. 13.3 - Prob. 6WECh. 13.3 - Prob. 7WECh. 13.3 - Prob. 8WECh. 13.3 - Prob. 9WECh. 13.3 - Prob. 10WECh. 13.3 - Prob. 11WECh. 13.3 - Prob. 12WECh. 13.3 - Prob. 13WECh. 13.3 - Prob. 14WECh. 13.3 - Prob. 15WECh. 13.3 - Prob. 16WECh. 13.3 - Prob. 17WECh. 13.3 - Prob. 18WECh. 13.3 - Prob. 19WECh. 13.3 - Prob. 20WECh. 13.3 - Prob. 21WECh. 13.3 - Prob. 22WECh. 13.3 - Prob. 23WECh. 13.3 - Prob. 24WECh. 13.3 - Prob. 25WECh. 13.3 - Prob. 26WECh. 13.3 - Prob. 27WECh. 13.3 - Prob. 28WECh. 13.3 - Prob. 29WECh. 13.3 - Prob. 30WECh. 13.3 - Prob. 1MRECh. 13.3 - Prob. 2MRECh. 13.3 - Prob. 3MRECh. 13.3 - Prob. 4MRECh. 13.3 - Prob. 5MRECh. 13.3 - Prob. 6MRECh. 13.3 - Prob. 7MRECh. 13.3 - Prob. 8MRECh. 13.3 - Prob. 9MRECh. 13.3 - Prob. 10MRECh. 13.3 - Prob. 11MRECh. 13.3 - Prob. 12MRECh. 13.4 - Prob. 1OECh. 13.4 - Prob. 2OECh. 13.4 - Prob. 3OECh. 13.4 - Prob. 4OECh. 13.4 - Prob. 5OECh. 13.4 - Prob. 6OECh. 13.4 - Prob. 7OECh. 13.4 - Prob. 8OECh. 13.4 - Prob. 9OECh. 13.4 - Prob. 10OECh. 13.4 - Prob. 11OECh. 13.4 - 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Prob. 48WECh. 13.5 - Prob. 1OECh. 13.5 - Prob. 2OECh. 13.5 - Prob. 3OECh. 13.5 - Prob. 4OECh. 13.5 - Prob. 5OECh. 13.5 - Prob. 6OECh. 13.5 - Prob. 7OECh. 13.5 - Prob. 8OECh. 13.5 - Prob. 9OECh. 13.5 - Prob. 10OECh. 13.5 - Prob. 11OECh. 13.5 - Prob. 12OECh. 13.5 - Prob. 13OECh. 13.5 - Prob. 14OECh. 13.5 - Prob. 15OECh. 13.5 - Prob. 16OECh. 13.5 - Prob. 1WECh. 13.5 - Prob. 2WECh. 13.5 - Prob. 3WECh. 13.5 - Prob. 4WECh. 13.5 - Prob. 5WECh. 13.5 - Prob. 6WECh. 13.5 - Prob. 7WECh. 13.5 - Prob. 8WECh. 13.5 - Prob. 9WECh. 13.5 - Prob. 10WECh. 13.5 - Prob. 11WECh. 13.5 - Prob. 12WECh. 13.5 - Prob. 13WECh. 13.5 - Prob. 14WECh. 13.5 - Prob. 15WECh. 13.5 - Prob. 16WECh. 13.5 - Prob. 17WECh. 13.5 - Prob. 18WECh. 13.5 - Prob. 19WECh. 13.5 - Prob. 20WECh. 13.5 - Prob. 21WECh. 13.5 - Prob. 22WECh. 13.5 - Prob. 23WECh. 13.5 - Prob. 24WECh. 13.5 - Prob. 25WECh. 13.5 - Prob. 26WECh. 13.5 - Prob. 27WECh. 13.5 - Prob. 28WECh. 13.5 - Prob. 29WECh. 13.5 - Prob. 1MRECh. 13.5 - Prob. 2MRECh. 13.5 - Prob. 3MRECh. 13.5 - Prob. 4MRECh. 13.5 - Prob. 5MRECh. 13.5 - Prob. 6MRECh. 13.5 - Prob. 7MRECh. 13.5 - Prob. 8MRECh. 13.5 - Prob. 1STCh. 13.5 - Prob. 2STCh. 13.5 - Prob. 3STCh. 13.5 - Prob. 4STCh. 13.5 - Prob. 5STCh. 13.5 - Prob. 6STCh. 13.5 - Prob. 7STCh. 13.6 - Prob. 1OECh. 13.6 - Prob. 2OECh. 13.6 - Prob. 3OECh. 13.6 - Prob. 4OECh. 13.6 - Prob. 5OECh. 13.6 - Prob. 6OECh. 13.6 - Prob. 7OECh. 13.6 - Prob. 8OECh. 13.6 - Prob. 9OECh. 13.6 - Prob. 10OECh. 13.6 - Prob. 11OECh. 13.6 - Prob. 12OECh. 13.6 - Prob. 13OECh. 13.6 - Prob. 14OECh. 13.6 - Prob. 1WECh. 13.6 - Prob. 2WECh. 13.6 - Prob. 3WECh. 13.6 - Prob. 4WECh. 13.6 - Prob. 5WECh. 13.6 - Prob. 6WECh. 13.6 - Prob. 7WECh. 13.6 - Prob. 8WECh. 13.6 - Prob. 9WECh. 13.6 - Prob. 10WECh. 13.6 - Prob. 11WECh. 13.6 - Prob. 12WECh. 13.6 - Prob. 13WECh. 13.6 - Prob. 14WECh. 13.6 - Prob. 15WECh. 13.6 - Prob. 16WECh. 13.6 - Prob. 17WECh. 13.6 - Prob. 18WECh. 13.6 - Prob. 19WECh. 13.6 - Prob. 20WECh. 13.6 - Prob. 21WECh. 13.6 - Prob. 22WECh. 13.6 - Prob. 23WECh. 13.6 - Prob. 24WECh. 13.6 - Prob. 25WECh. 13.6 - Prob. 26WECh. 13.6 - Prob. 27WECh. 13.6 - Prob. 28WECh. 13.6 - Prob. 29WECh. 13.6 - Prob. 30WECh. 13.6 - Prob. 31WECh. 13.6 - Prob. 32WECh. 13.6 - Prob. 33WECh. 13.6 - Prob. 34WECh. 13.6 - Prob. 35WECh. 13.6 - Prob. 36WECh. 13.6 - Prob. 37WECh. 13.6 - Prob. 38WECh. 13.6 - Prob. 39WECh. 13.6 - Prob. 40WECh. 13.6 - Prob. 41WECh. 13.6 - Prob. 42WECh. 13.6 - Prob. 43WECh. 13.6 - Prob. 44WECh. 13.6 - Prob. 45WECh. 13.6 - Prob. 46WECh. 13.6 - Prob. 47WECh. 13.6 - Prob. 48WECh. 13.6 - Prob. 49WECh. 13.6 - Prob. 50WECh. 13.6 - Prob. 51WECh. 13.6 - Prob. 52WECh. 13.6 - Prob. 53WECh. 13.6 - Prob. 54WECh. 13.6 - Prob. 55WECh. 13.6 - Prob. 56WECh. 13.6 - Prob. 57WECh. 13.6 - Prob. 58WECh. 13.7 - Prob. 1OECh. 13.7 - Prob. 2OECh. 13.7 - Prob. 3OECh. 13.7 - Prob. 4OECh. 13.7 - Prob. 5OECh. 13.7 - Prob. 6OECh. 13.7 - Prob. 7OECh. 13.7 - Prob. 8OECh. 13.7 - Prob. 9OECh. 13.7 - Prob. 10OECh. 13.7 - Prob. 11OECh. 13.7 - Prob. 12OECh. 13.7 - Prob. 13OECh. 13.7 - Prob. 14OECh. 13.7 - Prob. 15OECh. 13.7 - Prob. 16OECh. 13.7 - Prob. 1WECh. 13.7 - Prob. 2WECh. 13.7 - Prob. 3WECh. 13.7 - Prob. 4WECh. 13.7 - Prob. 5WECh. 13.7 - Prob. 6WECh. 13.7 - Prob. 7WECh. 13.7 - Prob. 8WECh. 13.7 - Prob. 9WECh. 13.7 - Prob. 10WECh. 13.7 - Prob. 11WECh. 13.7 - Prob. 12WECh. 13.7 - Prob. 13WECh. 13.7 - Prob. 14WECh. 13.7 - Prob. 15WECh. 13.7 - Prob. 16WECh. 13.7 - Prob. 17WECh. 13.7 - Prob. 18WECh. 13.7 - Prob. 19WECh. 13.7 - Prob. 20WECh. 13.7 - Prob. 21WECh. 13.7 - Prob. 22WECh. 13.7 - Prob. 23WECh. 13.7 - Prob. 24WECh. 13.7 - Prob. 25WECh. 13.7 - Prob. 26WECh. 13.7 - Prob. 27WECh. 13.7 - Prob. 28WECh. 13.7 - Prob. 29WECh. 13.7 - Prob. 30WECh. 13.7 - Prob. 31WECh. 13.7 - Prob. 32WECh. 13.7 - Prob. 33WECh. 13.7 - Prob. 34WECh. 13.7 - Prob. 35WECh. 13.7 - Prob. 36WECh. 13.7 - Prob. 37WECh. 13.7 - Prob. 1MRECh. 13.7 - Prob. 2MRECh. 13.7 - Prob. 3MRECh. 13.7 - Prob. 4MRECh. 13.7 - Prob. 5MRECh. 13.7 - Prob. 6MRECh. 13.7 - Prob. 7MRECh. 13.7 - Prob. 8MRECh. 13.7 - Prob. 9MRECh. 13.7 - Prob. 10MRECh. 13.7 - Prob. 11MRECh. 13.7 - Prob. 12MRECh. 13.7 - Prob. 1CECh. 13.7 - Prob. 2CECh. 13.7 - Prob. 3CECh. 13.7 - Prob. 4CECh. 13.8 - Prob. 1OECh. 13.8 - Prob. 2OECh. 13.8 - Prob. 3OECh. 13.8 - Prob. 4OECh. 13.8 - Prob. 5OECh. 13.8 - Prob. 6OECh. 13.8 - Prob. 7OECh. 13.8 - Prob. 8OECh. 13.8 - Prob. 9OECh. 13.8 - Prob. 10OECh. 13.8 - Prob. 11OECh. 13.8 - Prob. 12OECh. 13.8 - Prob. 1WECh. 13.8 - Prob. 2WECh. 13.8 - Prob. 3WECh. 13.8 - Prob. 4WECh. 13.8 - Prob. 5WECh. 13.8 - Prob. 6WECh. 13.8 - Prob. 7WECh. 13.8 - Prob. 8WECh. 13.8 - Prob. 9WECh. 13.8 - Prob. 10WECh. 13.8 - Prob. 11WECh. 13.8 - Prob. 12WECh. 13.8 - Prob. 13WECh. 13.8 - Prob. 14WECh. 13.8 - Prob. 15WECh. 13.8 - Prob. 16WECh. 13.8 - Prob. 17WECh. 13.8 - Prob. 18WECh. 13.8 - Prob. 19WECh. 13.8 - Prob. 20WECh. 13.8 - Prob. 21WECh. 13.8 - Prob. 22WECh. 13.8 - Prob. 23WECh. 13.8 - Prob. 24WECh. 13.8 - Prob. 25WECh. 13.8 - Prob. 26WECh. 13.8 - Prob. 27WECh. 13.8 - Prob. 28WECh. 13.8 - Prob. 29WECh. 13.8 - Prob. 30WECh. 13.8 - Prob. 31WECh. 13.8 - Prob. 32WECh. 13.8 - Prob. 33WECh. 13.8 - Prob. 34WECh. 13.8 - Prob. 35WECh. 13.8 - Prob. 36WECh. 13.8 - Prob. 37WECh. 13.8 - Prob. 38WECh. 13.8 - Prob. 39WECh. 13.8 - Prob. 40WECh. 13.8 - Prob. 41WECh. 13.8 - Prob. 42WECh. 13.8 - Prob. 43WECh. 13.9 - Prob. 1OECh. 13.9 - Prob. 2OECh. 13.9 - Prob. 3OECh. 13.9 - Prob. 4OECh. 13.9 - Prob. 5OECh. 13.9 - Prob. 6OECh. 13.9 - Prob. 7OECh. 13.9 - Prob. 8OECh. 13.9 - Prob. 9OECh. 13.9 - Prob. 10OECh. 13.9 - Prob. 11OECh. 13.9 - Prob. 1WECh. 13.9 - Prob. 2WECh. 13.9 - Prob. 3WECh. 13.9 - Prob. 4WECh. 13.9 - Prob. 5WECh. 13.9 - Prob. 6WECh. 13.9 - Prob. 7WECh. 13.9 - Prob. 8WECh. 13.9 - Prob. 9WECh. 13.9 - Prob. 10WECh. 13.9 - Prob. 11WECh. 13.9 - Prob. 12WECh. 13.9 - Prob. 13WECh. 13.9 - Prob. 14WECh. 13.9 - Prob. 15WECh. 13.9 - Prob. 16WECh. 13.9 - Prob. 17WECh. 13.9 - Prob. 18WECh. 13.9 - Prob. 19WECh. 13.9 - Prob. 20WECh. 13.9 - Prob. 21WECh. 13.9 - Prob. 22WECh. 13.9 - Prob. 23WECh. 13.9 - Prob. 24WECh. 13.9 - Prob. 25WECh. 13.9 - Prob. 26WECh. 13.9 - 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