Define tanh(t) in terms of exponentials

Whenever you have a define by exponentials question start with:

sinh(t)=0.5(et-e-t)      and    cosh(t)=0.5(et+e-t)

We know tanh(t)=sinh(t)/cosh(t)

               tanh(t)=0.5(et-e-t)/0.5(et+e-t)

                        =(et-e-t)/(et+e-t)  <=  0.5 cancels. This is the answer, though if you prefer, you can tidy it up by multiplying through by et

                        =(e2t-1)/(e2t+1)

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