Plot[{Cosh[x],Sinh[x]},{x,0,1}]

Plot[{Cosh[x],(1-Cosh[1])/Sinh[1]Sinh[x]},{x,0,1}]

Plot[{Cosh[x],(1-Cosh[1])/Sinh[1]Sinh[x],Cosh[x]+(1-Cosh[1])/Sinh[1]Sinh[x]},{x,0,1},
PlotStyle->{Dashed,}]