Define tanh(t) in terms of exponentials

Whenever you have a define by exponentials question start with:

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

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

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

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

                        =(e^2t-1)/(e^2t+1)