MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

simplify a trig expression


A direct substitution (with paper and pencil) gives that the integral of 
  Cos[x]/(Sin[x] + 1) is Log[Sin[x] + 1].  This is valid provided Sin[x] 
is not -1.

Mathematica gives:

   Integrate[Cos[x]/(Sin[x] + 1), x]
2 Log[Cos[x/2] + Sin[x/2]]

Is there some simple way to coerce the latter Mathematica-supplied 
result into the paper-and-pencil answer?

The closest I could get is:

   Log[TrigExpand[Expand[(Cos[x/2] + Sin[x/2])^2]]] /.
   {Sin[x/2] -> Sqrt[(1 - Cos[x])/2],
    Cos[x/2] -> Sqrt[(1 + Cos[x])/2]}
Log[1 + Sqrt[1 - Cos[x]]*Sqrt[1 + Cos[x]]]

Am I not seeing some easier TrigExpand or TrigReduce method?

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


  • Prev by Date: Re: How to use NMinimize with a numerical function
  • Next by Date: simultaneous nonlinear regression of a lot of data
  • Previous by thread: Rescale
  • Next by thread: simultaneous nonlinear regression of a lot of data