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Prove that sin [2 tan^(-1) {sqrt((1 -x)/...

Prove that `sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))`

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To prove that \[ \sin\left[2 \tan^{-1}\left(\sqrt{\frac{1 - x}{1 + x}}\right)\right] = \sqrt{1 - x^2}, \] we will follow a systematic approach. ...
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