The problem statement, all variables and given/known data Prove 2coth^(-1)(e^x) = ln[cosech x + coth x] The attempt at a solution I'm starting with the L.H.S. first, which is conventional, i think. 2coth^(-1)(e^x) = 2tanh^(-1)(e^-x) = 2[1/2 ln [(1+(e^-x))/(1-(e^-x))] = ln [(1+(e^-x))/(1-(e^-x))] I'm stuck. So, i tried to cheat a little, by expanding the R.H.S. and see if i could find a way to convert the last step above into the R.H.S. but my copybook has become something of a painting.