What is a Cartesian form for the parametric $(x,y)=\left(\sin(t)\cosh(t),\cos(t)\sinh(t)\right)$?

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What is a Cartesian form for the parametric $$(x,y)=\left(\sin(t)\cosh(t),\cos(t)\sinh(t)\right)$$ Does a Cartesian form exist?

I tried doing it by solving for t and substituting, but I don't believe it is possible to solve for t in this case. Do you have any other possible methods?