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Geometry Level 2

{x=asec3β tanβy=btan3β secβ\large \begin{cases} x = a \sec^3 \beta \ \tan \beta \\ y = b \tan^3 \beta \ \sec \beta \end{cases}

Given the above, find sin2β\sin^2 \beta.

Details and assumptions:

  • aa, bb, xx, yy, sinβ\sin\beta, cosβ0\cos\beta ≠ 0.
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