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The eccentric angles of the vertices of ...

The eccentric angles of the vertices of a triangle inscribed in the ellipse `x^2/a^2 + y^2/b^2 = 1` are `alpha, beta, gamma`. Show that its area is greatest when the angle subtended by two consecutive vertices of the triangle at the centre of the ellipse is `2pi/3`.

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The correct Answer is:
`2ab sin (alpha-beta)/(2) sin (beta-gamma)/(2)sin(gamma-alpha)/(2)`
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