Tanh of a sum

Theorem

The following formula holds: $$\mathrm{tanh}(z_1+z_2) = \dfrac{\tanh(z_1)+\tanh(z_2)}{1+\tanh(z_1)\tanh(z_2)},$$ where $\tanh$ denotes hyperbolic tangent.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.5.26$