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Question: simplifying a/sqrt(tan(x+c__1)^2+1);

Question:simplifying a/sqrt(tan(x+c__1)^2+1);

nm 9924 Maple 2024
simplify simplification trig
June 09 2024
2

How to make Maple simplify a/sqrt(tan(x+c__1)^2+1); to a/sqrt(sec(x+c__1)^2);  ?

Below is worksheet. since the second one is smaller in leaf size, expected simplify(...,size) to do it, But it did not. Any suggestions?

24832

> 

LC:=MmaTranslator:-Mma:-LeafCount;
e1:=a/sqrt(tan(x+c__1)^2+1);
e2:=a/sqrt(sec(x+c__1)^2);

MmaTranslator:-Mma:-LeafCount

a/(tan(x+c__1)^2+1)^(1/2)

a/(sec(x+c__1)^2)^(1/2)

> 

LC(e1);

12

> 

LC(e2);

10

> 

#we see they are same
simplify(e1-e2);

0

> 

#both nothing below make e1 to e2
simplify(e1); #not good simplification at all. Adds csgn.
LC(%);

a*csgn(sec(x+c__1))*cos(x+c__1)

11

> 

#expected this to do it but no
simplify(e1,size);
LC(%);

a/(tan(x+c__1)^2+1)^(1/2)

12

> 

simplify(e1,trig);

a/(tan(x+c__1)^2+1)^(1/2)

> 

combine(e1,trig);

a/(tan(x+c__1)^2+1)^(1/2)

> 

 


Using some other software:

 

 

 

Download tan_sec_simplification_june_9_2024.mw
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