       Re: simplify a trig expression

• To: mathgroup at smc.vnet.net
• Subject: [mg65433] Re: [mg65415] simplify a trig expression
• From: "Carl K. Woll" <carlw at wolfram.com>
• Date: Sat, 1 Apr 2006 05:38:52 -0500 (EST)
• References: <200603311109.GAA15029@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Murray Eisenberg wrote:
> 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?
>

Doesn't TrigReduce do whatyou want?

In:=
Log[TrigReduce[(Cos[x/2] + Sin[x/2])^2]]

Out=
Log[1+Sin[x]]

Carl Woll
WolframResearch

```

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