Feature request: cosh(asinh(x)) = sqrt(x^2+1)



Stavros Macrakis wrote:
> On Jan 22, 2008 10:08 AM, Raymond Toy (RT/EUS) <raymond.toy at ericsson.com 
> <mailto:raymond.toy at ericsson.com>> wrote:
> 
>      >> cosh(asinh(x)) = sqrt(x^2 + 1) 
> 
>  
> 
>     Should maxima already know this and if so, how
>     should it be done?  I think it would be easy to add this rule in
>     trigo.lisp, but is that the right thing to do?
> 
> 
> Sure, why not?  And the simplification should respect triginverses. I'm 

Mostly because rules are relatively simple to explain to people.  But I 
know lisp better than maxima, so for me, changing trigo is easier. :-)

> assuming no one wants the written-out forms of asinh(cosh(x)), 
> atan(sinh(x)), etc. to be built-in, though.  They are rather messy and 
> you might as well use logarc/exponentialize.

I was only thinking about cosh(asinh(x)) and sinh(acosh(x)).  Maybe a 
few others.  I'm not sure that sinh(acosh(x)) has the right branch cuts. 
  When I apply exponentialize, logarc, and ratsimp, I get 
sqrt(x-1)*sqrt(x+1).  I'll have to think about whether this result is 
correct....

Ray