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Prove that : (1-tan^2 (pi/4 - A))/(1+tan...

Prove that : `(1-tan^2 (pi/4 - A))/(1+tan^2 (pi/4 -A))= sin 2A`.

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To prove that \[ \frac{1 - \tan^2\left(\frac{\pi}{4} - A\right)}{1 + \tan^2\left(\frac{\pi}{4} - A\right)} = \sin(2A) \] we will start by simplifying the left-hand side. ...
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