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Re: Simplifying of rules


In a message dated 4/10/02 2:16:07 AM, fyzycyst at comcast.net writes:

>I got the following solution to a complicated set of trig equations (using
>the following statement: soln2 = Solve[{eq6, eq7}, a] where the equations
>involve trig functions of a, b and a+b ...
>
>{{a -> -ArcCos[-Cos[b]]}, {a -> ArcCos[-Cos[b]]},
> {a -> -ArcCos[Cos[b]]}, {a -> ArcCos[Cos[b]]}}
>
>Now, by inspection it's obvious what the relationship between a & b is,
>but
>how do I force Mathematica to simplify out all these ArcCos[Cos[]]
>instances?  
>
>I guess the other question would be "How could I have avoided these
>nonsimplified rules to begin with?"
>

The results that you expect imply some assumptions since they are not 
generally true

ArcCos[Cos[3Pi]]

Pi

soln = {{a->-ArcCos[-Cos[b]]},{a->ArcCos[-Cos[b]]},
           {a->-ArcCos[Cos[b]]},{a->
ArcCos[Cos[b]]}};

FullSimplify[soln /. -Cos[x_]->Cos[x], 0<=a<=Pi && 0<=b<=Pi]

{{a -> -b}, {a -> b}, {a -> -b}, {a -> b}}

soln /. -Cos[x_]->Cos[x] // PowerExpand

{{a -> -b}, {a -> b}, {a -> -b}, {a -> b}}


Bob Hanlon
Chantilly, VA  USA


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