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![if \: \: \tan( \alpha ) + \sin( \alpha ) = m \: and \: \tan( \alpha ) - \sin( \alpha ) = n \: \: then \: show \: that \: {m}^{2} - {n}^{2} = 4 \sqrt{mn} if \: \: \tan( \alpha ) + \sin( \alpha ) = m \: and \: \tan( \alpha ) - \sin( \alpha ) = n \: \: then \: show \: that \: {m}^{2} - {n}^{2} = 4 \sqrt{mn}](https://tex.z-dn.net/?f=if+%5C%3A++%5C%3A++%5Ctan%28+%5Calpha+%29++%2B++%5Csin%28+%5Calpha+%29++%3D+m+%5C%3A+and+%5C%3A++%5Ctan%28+%5Calpha+%29++-++%5Csin%28+%5Calpha+%29++%3D+n+%5C%3A++%5C%3A+then++%5C%3A+show+%5C%3A+that+%5C%3A++%7Bm%7D%5E%7B2%7D++-++%7Bn%7D%5E%7B2%7D++%3D+4+%5Csqrt%7Bmn%7D+)
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