Can anyone have idea how to proof the following relationship? \begin{equation} \sum_{j=1}^N \frac{\sinh(T-\tau j) + \sinh(\tau j)}{\sinh(T)} = \frac{\tanh(0.5T)}{\tanh(0.5\tau)}, \qquad \text{as}~N\rightarrow\infty, \end{equation} where $\tau:=T/N$.
Many thanks!