If \( x=\cot A+\cos A \) and \( y=\cot A-\cos A \) then prove that \[\left(\frac{x-y}{x+y}\right...

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If \( x=\cot A+\cos A \) and \( y=\cot A-\cos A \) then prove that
\[\left(\frac{x-y}{x+y}\right)^{2}+\left(\frac{x-y}{2}\right)^{2}=1 \text {. }\]
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