Re: Simplifying of rules

*To*: mathgroup at smc.vnet.net*Subject*: [mg33761] Re: [mg33742] Simplifying of rules*From*: BobHanlon at aol.com*Date*: Thu, 11 Apr 2002 02:14:20 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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