Stuck on a trigonometric identity proof....

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Discussion Overview

The discussion revolves around proving the trigonometric identity $\frac{1 -\cos A}{1 + \cos A} = (\cot A - \csc A)^2$. Participants explore various approaches to demonstrate this identity, focusing on algebraic manipulations and transformations involving trigonometric functions.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant states the identity to be proven: $\frac{1 -\cos A}{1 + \cos A} = (\cot A - \csc A)^2$.
  • Another participant asks what methods have been attempted so far to prove the identity.
  • A different approach is suggested, involving rewriting the cotangent and cosecant in terms of sine and cosine before performing operations on the right side.
  • Another participant proposes multiplying the left side by a form of one to simplify it, leading to an expression involving sine squared in the denominator.
  • One participant expresses gratitude and indicates they have successfully understood the proof after the discussion.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on a single method for proving the identity, as multiple approaches are suggested without a definitive resolution.

Contextual Notes

Participants do not clarify specific assumptions or limitations in their approaches, and the steps in the proofs remain unresolved.

Riwaj
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$\frac{1 -\cos A}{1 + \cos A} = (\cot A - \csc A)^2$
 
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Re: please prove it i am stuck ...

Riwaj said:
$\frac{1 -\cos A}{1 + \cos A} = (\cot A - \csc A)^2$
Hi Riwaj,

What did yo try so far ?
 
Re: please prove it i am stuck ...

My approach would be to change the cosecant and cotangent on the right side to sine and cosine, then do the indicated operations on the right.
 
Here's the start of another approach:

$$\frac{1 - \cos x}{1 + \cos x} \cdot \frac{1 - \cos x}{1 - \cos x} = \frac{1 - 2\cos x + \cos^2 x}{\sin^2 x}$$
 
oh ... thank you everyone i got it now
 

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