MHB Stuck on a trigonometric identity proof....

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The discussion revolves around proving the trigonometric identity $\frac{1 -\cos A}{1 + \cos A} = (\cot A - \csc A)^2$. Participants suggest transforming the right side into sine and cosine terms for simplification. One user demonstrates a method by multiplying the left side by $\frac{1 - \cos A}{1 - \cos A}$ to facilitate the proof. Ultimately, the user expresses gratitude after successfully solving the problem. The exchange highlights collaborative problem-solving in trigonometric proofs.
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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