2.26 The reciprocal hyperbolic functions

The reciprocal hyperbolic functions are defined by

where we take $x\neq 0$ to ensure that $\sinh x\neq 0$ and $\tanh x\neq 0$. These are sometimes called the hyperbolic secant, hyperbolic cosecant and hyperbolic cotangent functions; they should not be confused with the inverse hyperbolic functions, which are described in the workshop and assessed exercises.