MathGroup Archive 2006

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

Search the Archive

Re: Re: Trigonometric simplification


carlos at colorado.edu wrote:
>>Hi Carlos,
>>
>>Using TrigReduce before Simplify will do it:
>>
>>r = Tan[a]^2/(Sec[a]^2)^(3/2);
>>Simplify[TrigReduce[r], Assumptions -> {a > 0, Sec[a] > 0}]
>>
>>--> Cos[a]*Sin[a]^2
>>
>>Best regards,
>>Jean-Marc
> 
> 
> Thanks, that works perfectly.  Actually Sec[a]>0 as assumption
> is sufficient. This is correct from the problem source, since
> the angle is in the range (-Pi/2,Pi/2)

One wonders why that important bit of information was not in the 
original message. Or how you passed it to Simplify:

In[8]:= Simplify[Tan[a]^2/(Sec[a]^2)^(3/2),
   Assumptions->-Pi/2<a<Pi/2] // InputForm
Out[8]//InputForm= Cos[a]*Sin[a]^2


> Here is a related question.  How can I get Mathematica to pass from
> 
>    d = 2 + 3*Cos[a] + Cos[3*a]     (* leaf count 10 *)
> 
> to
> 
>     1 + 2*Cos[a]^3                  (* leaf count 8 *)
> 
> TrigExpand[d] gives
> 
>    2 + 3*Cos[a] + Cos[a]^3 - 3*Cos[a]*Sin[a]^2
> 
> Applying Simplify to that yields  2 + 3*Cos[a] + Cos[3*a]  so we are
> back to the beggining.


Thankfully, you can't.

In[1]:= d = 2 + 3*Cos[a] + Cos[3*a];

In[2]:= d2 = 1 + 2*Cos[a]^3;

In[3]:= Developer`ZeroQ[d-d2]
Out[3]= False

In[4]:= (d-d2) /. a->Pi/3 // N
Out[4]= 1.25

Offhand I do not know if there is a correct equivalent form that is 
simpler than the original.


Daniel Lichtblau
Wolfram Research




  • Prev by Date: Re: programming books / tutorials
  • Next by Date: General--Difficulties in Understanding Mathematica Syntax
  • Previous by thread: Re: Trigonometric simplification
  • Next by thread: Re: Re: Trigonometric simplification