An ellipse is inscribed in a rectangle and the angle between the diagonals of the rectangle is \....

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An ellipse is inscribed in a rectangle and the angle
\( \mathrm{P} \)
between the diagonals of the rectangle is
W
\( \tan ^{-1}(2 \sqrt{2}) \) then the eccentricity of the ellipse is
(1) \( \sqrt{2}-1 \)
(2) \( \frac{1}{\sqrt{2}} \)
(3) \( \frac{\sqrt{3}}{2} \)
(4) none of these



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