PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
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Chapter 5.5, Problem 83E
To determine

To represent: The expression sin(α+β)−sin(α−β) as a product using the sum-to-product formula.

Expert Solution & Answer
Check Mark

Answer to Problem 83E

The expression sin(α+β)−sin(α−β) can be represented as 2sinβcosα .

Explanation of Solution

Given information:

The given expression is sin(α+β)−sin(α−β) .

Calculation:

Consider the sum-to-product formula.

  sinu−sinv=2sin(u−v2)cos(u+v2)

Let the value of u is α+β and v is α−β from the given expression. Substitute these values in the above equation.

  sin(α+β)−sin(α−β)=2sin(α+β−(α−β)2)cos(α+β+α−β2)=2sin(2β2)cos(2α2)=2sinβcosα

Therefore, the expression sin(α+β)−sin(α−β) can be represented as 2sinβcosα .

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Chapter 5.5, Problem 82E
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Chapter 5.5, Problem 84E

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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