Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Chapter 5, Problem 125RE
To determine

Tocalculate:The sum or difference as a product by using the sum-to-product formulas.

Expert Solution & Answer
Check Mark

Answer to Problem 125RE

The required expression is 2cosxsinπ4 .

Explanation of Solution

Given information:

The expression =sin(x+π4)−sin(x−π4)

Formula used:

The sum-to-product formulas are:

  sinα+sinβ=2sinα+β2cosα−β2sinα−sinβ=2cosα+β2sinα−β2cosα+cosβ=2cosα+β2cosα−β2cosα−cosβ=−2sinα+β2sinα−β2

Calculation:

Know that, sinα−sinβ=2cosα+β2sinα−β2

To expand the given expression sin(x+π4)−sin(x−π4) , use the formula sinα−sinβ=2cosα+β2sinα−β2 .

Substitute x+π4 for α and x−π4 for β in the above formula.

  sin(x+π4)−sin(x−π4)=2cosx+π4+x−π42sinx+π4−x+π42=2cos2x2sin2π422=2cosxsinπ2×2=2cosxsinπ4

Hence, the required expression is 2cosxsinπ4 .

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Chapter 5, Problem 124RE
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Chapter 5, Problem 126RE

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

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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Propositional Logic, Propositional Variables & Compound Propositions; Author: Neso Academy;https://www.youtube.com/watch?v=Ib5njCwNMdk;License: Standard YouTube License, CC-BY
Propositional Logic - Discrete math; Author: Charles Edeki - Math Computer Science Programming;https://www.youtube.com/watch?v=rL_8y2v1Guw;License: Standard YouTube License, CC-BY
DM-12-Propositional Logic-Basics; Author: GATEBOOK VIDEO LECTURES;https://www.youtube.com/watch?v=pzUBrJLIESU;License: Standard Youtube License
Lecture 1 - Propositional Logic; Author: nptelhrd;https://www.youtube.com/watch?v=xlUFkMKSB3Y;License: Standard YouTube License, CC-BY
MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY