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Re: Mistake in applying a rule

• To: mathgroup at smc.vnet.net
• Subject: [mg80677] Re: Mistake in applying a rule
• From: Szabolcs <szhorvat at gmail.com>
• Date: Tue, 28 Aug 2007 06:41:33 -0400 (EDT)
• Organization: University of Bergen
• References: <fb0f17$f05$1@smc.vnet.net>

Steven Siew wrote:
> Hi,
> 
>   I'm trying to show that Integrate[Cos[x-a]] is Sin[x-a] + C
> 
>   I manage to get Simplify @ Integrate[Cos[x-a]] to give -Sin[a-x]
> 
>   This is fine because Sin[-x] is equal to -Sin[x]
> 
>   But when I apply the rule Times[-1,Sin[Plus[g_,Times[-1,h_]]]] ->
> Sin[h-g]  it fails.

Hi,

Your replacement rule is working correctly, however, for some reason 
Mathematica likes to sort the variables inside the Sin[], and take the 
minus sign out.  For example, try the following:

In[1]:= Sin[b-a]
Out[1]= -Sin[a-b]

In[2]:= Cos[b-a]
Out[2]= Cos[a-b]

In[3]:= f[b-a]
Out[3]= f[-a+b]

Szabolcs