Beautiful Area Between The Lines And The Curve

Calculus Level 4

In the above graph, the red curve is a part of the curve $$x^2-y^2=1$$ (mostly in the first quadrant). A point $$A$$ lies on this red curve and is connected to the origin by the green line segment.

If the $$x$$-coordinate of point $$A$$ equals $$\dfrac{e^{2016}+e^{-2016}}{2}$$, find the area bounded by the red curve, green line segment and the black $$x$$-axis in the first quadrant.

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