u=TANH(X/2), EXPRESS SINH X IN TERMS OF U

Question

u=TANH(X/2), EXPRESS SINH X IN TERMS OF U

Answer 1

 

There is a half-angle equation for tanh() that relates tanh(x/2) to sinh(x) and cosh(x):

 

   tanh(x/2) = sinh(x) / (1+cosh(x))

 

 

This can be rearranged to   

   sinh(x) = tanh(x/2) (1+cosh(x))  

 

Technically, that expresses sinh(x) as u=tanh(x/2), but perhaps they want more(?)