Thread: hyperbolic function

sinh(x) = [e^x -e^(-x)] / 2

So,
sinh(ln(t))

= [e^(ln(t)) -e^(-ln(t))] / 2

= [t -1/t] / 2

= [(t^2 -1)/t] / 2

= (t^2 -1) / (2t) ---------------answer.

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e^(-ln(t))
= e^(ln(t^(-1)))
= e^(ln(1/t))
= 1/t