How Can You Factor the Trigonometric Expression sin^3(x)-cos^3(x)?

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Homework Help Overview

The discussion revolves around factoring the trigonometric expression sin3(x) - cos3(x). Participants are exploring the relationship between the terms and potential identities that may apply.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the correctness of an initial proposed equality involving the expression and discussing the use of trigonometric identities, such as sin2(x) + cos2(x) = 1. There is also a suggestion to factor the numerator to aid in the solution.

Discussion Status

The discussion is ongoing, with participants clarifying their understanding of the expression and exploring different interpretations. Some guidance has been offered regarding factoring and the use of identities, but no consensus has been reached on the correct approach or solution.

Contextual Notes

Participants express uncertainty about the initial equality and the appropriate steps to take, indicating a lack of clarity in the problem setup.

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Homework Statement



sin^3(x)-cos^3(x)
sin(x) - cos(x)

equals

1 + sin(x) + cos(x)

Homework Equations


Not sure :/


The Attempt at a Solution


Not sure where to even start.
 
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Are you sure that it's 1+sin(x)+cos(x) and not 1+sin(x)cos(x)?

Use the identity sin^2(x)+cos^2(x)=1.
 
Oh yeah, that was it.
 
sin^3(x)-cos^3(x)
-----------------
sin(x) - cos(x)

Try factoring the numerator, it may help you.
 

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