Date: Mar 24, 2013 4:35 AM
Author: Nasser Abbasi
Subject: Handling branch cuts in trig functions

I tried to simplify sqrt( sec(x)^2 ) but Mathematica will
only do this by assuming x is inside one branch, say
x>-Pi/2 && x<Pi/2 but Maple and maxima simplified it
but they gave the answer is terms of |sec(x)| to take
care of the sign which depends on the branch.

Here is plot of sec(x)

In[37]:= Assuming[x>-Pi/2&&x<Pi/2,Simplify[Sqrt[Sec[x]^2]]]
Out[37]= Sec[x]

In[39]:= Assuming[x > Pi/2 && x < Pi, Simplify[Sqrt[Sec[x]^2]]]
Out[39]= -Sec[x]

If I just tell M that x>0, it will not simplify it.

In[38]:= Assuming[x>0,Simplify[Sqrt[Sec[x]^2]]]
Out[38]= Sqrt[Sec[x]^2]

but Maple did it only with the x>0 assumption:

simplify(sqrt(sec(x)^2)) assuming x::positive;

/ 1 \

On maxima 12.04.0


I think now that answer to sqrt(sec(x)^2) should be
|sec(x)| without need to give the branch. Since the only
different is the sign. Or is there something else here?