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\( P \) is any point lying on the ellipse
\( \mathrm{P}^{\prime \prime} \) \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(ab) \) whose foci and \( S \) and \( S \). If

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\( \angle P S S^{\prime}=\alpha \) and \( \angle P S^{\prime} S=\beta \), then the value of \( \tan \frac{\alpha}{2} \tan \frac{\beta}{2} \) is:
(1) \( \frac{1+e}{1-e} \)
(2) \( \frac{1-e^{2}}{1-e^{2}} \)
(3) \( \frac{1-e}{1+e} \)
(4) 1
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