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José Antonio Díaz Navas
José Antonio Díaz Navas
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$Assumptions = Element[t, Reals] && Element[ω, Reals] && ω > 0 
&& t > 0;
ArcTan[8.54596*10^7 (1. + 1. t^2 ω^2) (1.2214 + E^ω Cos[
2 ArcTan[t ω]]), -1.70919*10^8 E^ω t ω] + 
ArcTan[8.54596*10^7 (1. + 1. t^2 ω^2) (1.2214 + E^ω 
Cos[2ArcTan[t ω]]),1.70919*10^8 E^ω t ω]//FullSimplify

Mathematica doesn't simplify this seemingly ArcTan[x,y]+ArcTan[x,-y]ArcTan[x,y]+ArcTan[x,-y] expression. I plotted the 3D-graph, it shows the expression is zero for all values of tt and $\omega$\[Omega].

I understand one underlying reason might be Mathematica isn't sure about the positivity of CosCos term in "x"x, and hence, "x"x. Am I right? Any ideas to simplify this term in code, instead of manually, would be very much appreciated. I'm relatively new to the language.

$Assumptions = Element[t, Reals] && Element[ω, Reals] && ω > 0 
&& t > 0;
ArcTan[8.54596*10^7 (1. + 1. t^2 ω^2) (1.2214 + E^ω Cos[
2 ArcTan[t ω]]), -1.70919*10^8 E^ω t ω] + 
ArcTan[8.54596*10^7 (1. + 1. t^2 ω^2) (1.2214 + E^ω 
Cos[2ArcTan[t ω]]),1.70919*10^8 E^ω t ω]//FullSimplify

Mathematica doesn't simplify this seemingly ArcTan[x,y]+ArcTan[x,-y] expression. I plotted the 3D-graph, it shows the expression is zero for all values of t and $\omega$.

I understand one underlying reason might be Mathematica isn't sure about the positivity of Cos term in "x", and hence, "x". Am I right? Any ideas to simplify this term in code, instead of manually, would be very much appreciated. I'm relatively new to the language.

$Assumptions = Element[t, Reals] && Element[ω, Reals] && ω > 0 
&& t > 0;
ArcTan[8.54596*10^7 (1. + 1. t^2 ω^2) (1.2214 + E^ω Cos[
2 ArcTan[t ω]]), -1.70919*10^8 E^ω t ω] + 
ArcTan[8.54596*10^7 (1. + 1. t^2 ω^2) (1.2214 + E^ω 
Cos[2ArcTan[t ω]]),1.70919*10^8 E^ω t ω]//FullSimplify

Mathematica doesn't simplify this seemingly ArcTan[x,y]+ArcTan[x,-y] expression. I plotted the 3D-graph, it shows the expression is zero for all values of t and \[Omega].

I understand one underlying reason might be Mathematica isn't sure about the positivity of Cos term in x, and hence, x. Am I right? Any ideas to simplify this term in code, instead of manually, would be very much appreciated. I'm relatively new to the language.

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Henrik Schumacher
Henrik Schumacher
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$Assumptions = Element[t, Reals] && Element[\[Omega]Element[ω, Reals] && \[Omega]ω > 0 
&& t > 0;
ArcTan[8.54596*10^7 (1. + 1. t^2 \[Omega]^2ω^2) (1.2214 + E^\[Omega]E^ω Cos[
2 ArcTan[t \[Omega]]]ω]]), -1.70919*10^8 E^\[Omega]E^ω t \[Omega]]ω] + 
ArcTan[8.54596*10^7 (1. + 1. t^2 \[Omega]^2ω^2) (1.2214 + E^\[Omega]E^ω 
Cos[2ArcTan[t \[Omega]]]ω]]),1.70919*10^8 E^\[Omega]E^ω t \[Omega]]ω]//FullSimplify

Mathematica doesn't simplify this seemingly ArcTan[x,y]+ArcTan[x,-y] expression. I plotted the 3D-graph, it shows the expression is zero for all values of t and $\omega$.

I understand one underlying reason might be Mathematica isn't sure about the positivity of Cos term in "x", and hence, "x". Am I right? Any ideas to simplify this term in code, instead of manually, would be very much appreciated. I'm relatively new to the language.

$Assumptions = Element[t, Reals] && Element[\[Omega], Reals] && \[Omega] > 0 
&& t > 0;
ArcTan[8.54596*10^7 (1. + 1. t^2 \[Omega]^2) (1.2214 + E^\[Omega] Cos[
2 ArcTan[t \[Omega]]]), -1.70919*10^8 E^\[Omega] t \[Omega]] + 
ArcTan[8.54596*10^7 (1. + 1. t^2 \[Omega]^2) (1.2214 + E^\[Omega] 
Cos[2ArcTan[t \[Omega]]]),1.70919*10^8 E^\[Omega] t \[Omega]]//FullSimplify

Mathematica doesn't simplify this seemingly ArcTan[x,y]+ArcTan[x,-y] expression. I plotted the 3D-graph, it shows the expression is zero for all values of t and $\omega$.

I understand one underlying reason might be Mathematica isn't sure about the positivity of Cos term in "x", and hence, "x". Am I right? Any ideas to simplify this term in code, instead of manually, would be very much appreciated. I'm relatively new to the language.

$Assumptions = Element[t, Reals] && Element[ω, Reals] && ω > 0 
&& t > 0;
ArcTan[8.54596*10^7 (1. + 1. t^2 ω^2) (1.2214 + E^ω Cos[
2 ArcTan[t ω]]), -1.70919*10^8 E^ω t ω] + 
ArcTan[8.54596*10^7 (1. + 1. t^2 ω^2) (1.2214 + E^ω 
Cos[2ArcTan[t ω]]),1.70919*10^8 E^ω t ω]//FullSimplify

Mathematica doesn't simplify this seemingly ArcTan[x,y]+ArcTan[x,-y] expression. I plotted the 3D-graph, it shows the expression is zero for all values of t and $\omega$.

I understand one underlying reason might be Mathematica isn't sure about the positivity of Cos term in "x", and hence, "x". Am I right? Any ideas to simplify this term in code, instead of manually, would be very much appreciated. I'm relatively new to the language.

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naeema18
naeema18
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Simplifying this ArcTan sum expression

$Assumptions = Element[t, Reals] && Element[\[Omega], Reals] && \[Omega] > 0 
&& t > 0;
ArcTan[8.54596*10^7 (1. + 1. t^2 \[Omega]^2) (1.2214 + E^\[Omega] Cos[
2 ArcTan[t \[Omega]]]), -1.70919*10^8 E^\[Omega] t \[Omega]] + 
ArcTan[8.54596*10^7 (1. + 1. t^2 \[Omega]^2) (1.2214 + E^\[Omega] 
Cos[2ArcTan[t \[Omega]]]),1.70919*10^8 E^\[Omega] t \[Omega]]//FullSimplify

Mathematica doesn't simplify this seemingly ArcTan[x,y]+ArcTan[x,-y] expression. I plotted the 3D-graph, it shows the expression is zero for all values of t and $\omega$.

I understand one underlying reason might be Mathematica isn't sure about the positivity of Cos term in "x", and hence, "x". Am I right? Any ideas to simplify this term in code, instead of manually, would be very much appreciated. I'm relatively new to the language.