Pretty difficult trig proof (identity)

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SUMMARY

The discussion focuses on the trigonometric identity proof involving the equation \(\frac{\sin\theta}{1-\cos\theta} - \frac{\cot\theta}{1+\cos\theta} = \frac{1-\cos^{3}\theta}{\sin^{3}\theta}\). Participants analyze the steps taken by the Original Poster (OP) and identify errors in the manipulation of terms, particularly regarding the treatment of the cotangent function and common factors. The consensus emphasizes the importance of correctly applying trigonometric identities and recognizing common factors in both the numerator and denominator.

PREREQUISITES
  • Understanding of basic trigonometric identities
  • Familiarity with the cotangent function
  • Ability to manipulate algebraic fractions
  • Knowledge of common factor extraction in expressions
NEXT STEPS
  • Study the derivation of trigonometric identities
  • Practice problems involving the cotangent function
  • Learn techniques for simplifying algebraic fractions
  • Explore common mistakes in trigonometric proofs and how to avoid them
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone seeking to improve their problem-solving skills in trigonometric proofs.

iRaid
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Homework Statement


\frac{sin\theta}{1-cos\theta} - \frac{cot\theta}{1+cos\theta} = \frac{1-cos^{3}\theta}{sin^{3}\theta}


Homework Equations


Trig identities..


The Attempt at a Solution


Basically I got to:
\frac{sin\theta+(cos^{2}\theta)(sin\theta)}{sin^{2}\theta}

Homework Statement



Is that right up to there, I think not because I can't get passed this lol.


Homework Equations





The Attempt at a Solution

 
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That doesn't look right.

Show how you got your result so we can help you.
 
iRaid said:

Homework Statement


\frac{sin\theta}{1-cos\theta} - \frac{cot\theta}{1+cos\theta} = \frac{1-cos^{3}\theta}{sin^{3}\theta}


Homework Equations


Trig identities..


The Attempt at a Solution


Basically I got to:
\frac{sin\theta+(cos^{2}\theta)(sin\theta)}{sin^{2}\theta}

Homework Statement



Is that right up to there, I think not because I can't get passed this lol.


Homework Equations





The Attempt at a Solution


You did notice the cot function did you - or did you misread it as cos?
 
I don't think you were supposed to solve the question for the Original Poster!
 
Last edited by a moderator:
>_> Oh. Well, I hope my explanation blurb thing helps so that I'm not just blatantly giving the solution without providing any real understanding.
 
Dr. Seafood said:
>_> Oh. Well, I hope my explanation blurb thing helps so that I'm not just blatantly giving the solution without providing any real understanding.
PeterO is correct. The Physics Forums rules do not permit a member to post the solution to another member's problem.
 
OK, I attached the rest of my work..
 

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iRaid said:
OK, I attached the rest of my work..

In your 5th line, when you took out a factor of sin(theta) in the numerator, it was not a common factor, as it was in the denominator of a couple of the terms.
 
PeterO said:
In your 5th line, when you took out a factor of sin(theta) in the numerator, it was not a common factor, as it was in the denominator of a couple of the terms.

I see now thanks, I got it. Stupid mistakes.
 

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