Proving this trignometric identity

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Homework Help Overview

The discussion revolves around proving a trigonometric identity involving cosine and sine functions. The original poster presents an equation that needs to be validated, suggesting a connection to the double angle formula.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants suggest expanding the expression \((1-\cos(x))^2\) and expressing \(\sin(x/2)\) in terms of sine and cosine. There is a focus on the use of the double angle formula and its implications for the identity.

Discussion Status

Some participants have offered guidance on potential approaches, such as using the double angle formula and expanding certain expressions. However, there is no explicit consensus on the method to be employed, and questions about the specifics of these approaches remain open.

Contextual Notes

The original poster notes a lack of equations that could assist in the proof, indicating a potential constraint in available methods or information. There is also a discussion about the appropriateness of expanding in terms of \(\sin(x)/\cos(x)\), which suggests varying interpretations of the problem setup.

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Homework Statement



Prove that :

[itex]\frac{cos(x)-1}{(1-cos(x))^{3}}[/itex] = -[itex]\frac{1}{4sin^{4}(0.5x)}[/itex]

Homework Equations



None that I can think of.
Maybe the double angle formula...

The Attempt at a Solution



I couldn't do much in this question :

-[itex]\frac{1}{(1-cos(x))^{2}}[/itex]
 
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Things to try: expand [itex](1-\cos(x))^2[/itex] and expressing [itex]\sin(x/2)[/itex] in terms of just sin and cos.
 
Yes, use the double angle formula.

ehild
 
micromass said:
...and expressing [itex]\sin(x/2)[/itex] in terms of just sin and cos.

What exactly do you mean by that ?

Should I expand it in powers of Sin(x)/Cos(x) ?
 
hms.tech said:
What exactly do you mean by that ?

Should I expand it in powers of Sin(x)/Cos(x) ?

Use double angle formula. What is cos(2x) in terms of sin? Similarly, what is cos(x)?
 

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