how can I simplify sqrt(1-sin(x)*sin(x)) to |cos(x)|



One of the problems in this case is that the sqrt is not equal to the value
you wish to replace it with.
The sqrt function sqrt(x^2) has two values, x and -x.  Each of them is a
function that is continuous and differentiable.  |x| is not equal to either
of these functions.



> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:maxima-
> bounces at math.utexas.edu] On Behalf Of Stavros Macrakis
> Sent: Friday, September 22, 2006 7:06 AM
> To: maxima at math.utexas.edu
> Cc: xiaolei zhang
> Subject: Re: [Maxima] how can I simplify sqrt(1-sin(x)*sin(x)) to |cos(x)|
> 
> > I an new to maxiam, how can I simplify sqrt(1-sin(x)*sin(x)) to |cos(x)|
> 
> Unfortunately, there is no completely automatic way to do this, but
> here are a couple of approaches.
> 
> expr: sqrt(1-sin(x)*sin(x))$
> 
> substpart(trigsimp(piece),expr,1);
>         Simplifies the part within the sqrt.
> 
> substpart(trigrat(piece),expr,1);
>         Simplifies the part within the sqrt.
> 
> trigrat(radcan(exponentialize(expr)));
>         Convert to exponential form, simplify the exponentials, and
> convert to trigonometric form.
> 
> There are other approaches to try in other cases as well....
> 
>              -s
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