A curve is in the first quadrant. It has parametric equations \(x = \cosh t + \sinh t , y = \cosh t - \sinh t\) where \(t \in \mathbb { R }\). Show that the cartesian equation of the curve is \(x y = 1\).
Fig. 6 shows the curve from part (i). P is a point on the curve. O is the origin. Point A lies on the \(x\)-axis, point B lies on the \(y\)-axis and OAPB is a rectangle.
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