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arctg(1/x)=O(1) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
    /1\    
atan|-| = o
    \x/
atan⁡(1x)=o\operatorname{atan}{\left(\frac{1}{x} \right)} = o
Simplificar
Gráfica
Respuesta rápida [src] 
                                                sin(2*re(o))                                                                                       I*sinh(2*im(o))                                          
x1 = -------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------
     /            2                                  2                 \                                  /            2                                  2                 \                               
     |         sin (2*re(o))                     sinh (2*im(o))        |                                  |         sin (2*re(o))                     sinh (2*im(o))        |                               
     |------------------------------- + -------------------------------|*(cos(2*re(o)) + cosh(2*im(o)))   |------------------------------- + -------------------------------|*(cos(2*re(o)) + cosh(2*im(o)))
     |                              2                                 2|                                  |                              2                                 2|                               
     \(cos(2*re(o)) + cosh(2*im(o)))    (cos(2*re(o)) + cosh(2*im(o))) /                                  \(cos(2*re(o)) + cosh(2*im(o)))    (cos(2*re(o)) + cosh(2*im(o))) /
x1=sin⁡(2re⁡(o))(sin⁡2(2re⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2+sinh⁡2(2im⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2)(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))−isinh⁡(2im⁡(o))(sin⁡2(2re⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2+sinh⁡2(2im⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2)(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))x_{1} = \frac{\sin{\left(2 \operatorname{re}{\left(o\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)} - \frac{i \sinh{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)} 
x1 = sin(2*re(o))/((sin(2*re(o))^2/(cos(2*re(o)) + cosh(2*im(o)))^2 + sinh(2*im(o))^2/(cos(2*re(o)) + cosh(2*im(o)))^2)*(cos(2*re(o)) + cosh(2*im(o)))) - i*sinh(2*im(o))/((sin(2*re(o))^2/(cos(2*re(o)) + cosh(2*im(o)))^2 + sinh(2*im(o))^2/(cos(2*re(o)) + cosh(2*im(o)))^2)*(cos(2*re(o)) + cosh(2*im(o))))
Suma y producto de raíces [src] 
suma
                                           sin(2*re(o))                                                                                       I*sinh(2*im(o))                                          
-------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------
/            2                                  2                 \                                  /            2                                  2                 \                               
|         sin (2*re(o))                     sinh (2*im(o))        |                                  |         sin (2*re(o))                     sinh (2*im(o))        |                               
|------------------------------- + -------------------------------|*(cos(2*re(o)) + cosh(2*im(o)))   |------------------------------- + -------------------------------|*(cos(2*re(o)) + cosh(2*im(o)))
|                              2                                 2|                                  |                              2                                 2|                               
\(cos(2*re(o)) + cosh(2*im(o)))    (cos(2*re(o)) + cosh(2*im(o))) /                                  \(cos(2*re(o)) + cosh(2*im(o)))    (cos(2*re(o)) + cosh(2*im(o))) /
sin⁡(2re⁡(o))(sin⁡2(2re⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2+sinh⁡2(2im⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2)(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))−isinh⁡(2im⁡(o))(sin⁡2(2re⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2+sinh⁡2(2im⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2)(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))\frac{\sin{\left(2 \operatorname{re}{\left(o\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)} - \frac{i \sinh{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)} 
=
                                           sin(2*re(o))                                                                                       I*sinh(2*im(o))                                          
-------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------
/            2                                  2                 \                                  /            2                                  2                 \                               
|         sin (2*re(o))                     sinh (2*im(o))        |                                  |         sin (2*re(o))                     sinh (2*im(o))        |                               
|------------------------------- + -------------------------------|*(cos(2*re(o)) + cosh(2*im(o)))   |------------------------------- + -------------------------------|*(cos(2*re(o)) + cosh(2*im(o)))
|                              2                                 2|                                  |                              2                                 2|                               
\(cos(2*re(o)) + cosh(2*im(o)))    (cos(2*re(o)) + cosh(2*im(o))) /                                  \(cos(2*re(o)) + cosh(2*im(o)))    (cos(2*re(o)) + cosh(2*im(o))) /
sin⁡(2re⁡(o))(sin⁡2(2re⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2+sinh⁡2(2im⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2)(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))−isinh⁡(2im⁡(o))(sin⁡2(2re⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2+sinh⁡2(2im⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2)(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))\frac{\sin{\left(2 \operatorname{re}{\left(o\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)} - \frac{i \sinh{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)} 
producto
                                           sin(2*re(o))                                                                                       I*sinh(2*im(o))                                          
-------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------
/            2                                  2                 \                                  /            2                                  2                 \                               
|         sin (2*re(o))                     sinh (2*im(o))        |                                  |         sin (2*re(o))                     sinh (2*im(o))        |                               
|------------------------------- + -------------------------------|*(cos(2*re(o)) + cosh(2*im(o)))   |------------------------------- + -------------------------------|*(cos(2*re(o)) + cosh(2*im(o)))
|                              2                                 2|                                  |                              2                                 2|                               
\(cos(2*re(o)) + cosh(2*im(o)))    (cos(2*re(o)) + cosh(2*im(o))) /                                  \(cos(2*re(o)) + cosh(2*im(o)))    (cos(2*re(o)) + cosh(2*im(o))) /
sin⁡(2re⁡(o))(sin⁡2(2re⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2+sinh⁡2(2im⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2)(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))−isinh⁡(2im⁡(o))(sin⁡2(2re⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2+sinh⁡2(2im⁡(o))(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))2)(cos⁡(2re⁡(o))+cosh⁡(2im⁡(o)))\frac{\sin{\left(2 \operatorname{re}{\left(o\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)} - \frac{i \sinh{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\left(\frac{\sin^{2}{\left(2 \operatorname{re}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}} + \frac{\sinh^{2}{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)^{2}}\right) \left(\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}\right)} 
=
 cos(2*re(o)) + cosh(2*im(o)) 
------------------------------
I*sinh(2*im(o)) + sin(2*re(o))
cos⁡(2re⁡(o))+cosh⁡(2im⁡(o))sin⁡(2re⁡(o))+isinh⁡(2im⁡(o))\frac{\cos{\left(2 \operatorname{re}{\left(o\right)} \right)} + \cosh{\left(2 \operatorname{im}{\left(o\right)} \right)}}{\sin{\left(2 \operatorname{re}{\left(o\right)} \right)} + i \sinh{\left(2 \operatorname{im}{\left(o\right)} \right)}} 
(cos(2*re(o)) + cosh(2*im(o)))/(i*sinh(2*im(o)) + sin(2*re(o)))
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