Differentiate and simplify: f(x)=sin^2(2x)-cos^2(2x)

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Homework Help Overview

The discussion revolves around the differentiation and simplification of the function f(x) = sin²(2x) - cos²(2x), focusing on whether the expression has been fully simplified.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the simplification of the trigonometric expression, questioning if it can be expressed in a simpler form. Some express confidence in the current simplification, while others inquire about potential alternative forms.

Discussion Status

The discussion includes varying opinions on the simplification status, with some participants suggesting that the expression is fully simplified and others questioning the possibility of a simpler representation. There is a recognition of different perspectives on the use of trigonometric identities.

Contextual Notes

Participants reference trigonometric identities and express uncertainty about the completeness of the simplification, indicating a potential for multiple interpretations of the expression's simplicity.

ttpp1124
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Homework Statement
Has this been simplified fully?
Relevant Equations
n/a
Screen Shot 2020-05-11 at 10.11.17 PM.png
 
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ttpp1124 said:
Homework Statement:: Has this been simplified fully?
Relevant Equations:: n/a

View attachment 262618
Do you have a question here?
 
Is that an answer to the quesion in post #1 or the one in post #2 ? Or both ? :cool:

Let me ask @ttpp1124 : do you expect there exists a simpler expression ? In what way ?
 
Last edited:
yes, it is fully simplified, and of course with trig you could go in many circles with identities but I believe the one stopped at is simplest.
 
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Mark44 said:
Do you have a question here?
yes, sorry, I forgot to include the question! here it is:
 

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I would use [itex]\cos (2\theta) = \cos^2 \theta - \sin^2\theta[/itex], from which immediately [itex]y = -\cos(4x)[/itex].
 
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ttpp1124 said:
yes, sorry, I forgot to include the question! here it is:
Not much of a question !

Kudos @pasmith : the simplest path to the simplest result !
 

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