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cosh^2 x - sinh^2 x = 1 cosh x = 1+ sinh^2 x cosh x = 1+(-3/5)^2 cosh x = 1+9/25 = 34/25 cosh 2x = 2 sinh x cosh x cosh 2x = 2 (-3/5) (34/25) =-204/125
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The curve given by (t-sinh(t)cosh(t), 2 cosh(t)), t real.
It is cosh(x) + c where c is a constant of integration.
Let x = ea then 1/x = e-a where e is the base of natural logarithms. Then y = x + 1/x = ea + e-a So y/2 = (ea + e-a)/2 = cosh(a), the hyperbolic cosine function a = cosh-1(y/2) x= exp(cosh-1(y/2))