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cospi(x+1)/4=√2/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
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cos(p)*I*(x + 1)   \/ 2 
---------------- = -----
       4             2
icos⁡(p)(x+1)4=22\frac{i \cos{\left(p \right)} \left(x + 1\right)}{4} = \frac{\sqrt{2}}{2}
Simplificar
Solución detallada
Tenemos la ecuación
icos⁡(p)(x+1)4=22\frac{i \cos{\left(p \right)} \left(x + 1\right)}{4} = \frac{\sqrt{2}}{2}
cambiamos
i(x+1)cos⁡(p)4−1−22=0\frac{i \left(x + 1\right) \cos{\left(p \right)}}{4} - 1 - \frac{\sqrt{2}}{2} = 0
icos⁡(p)(x+1)4−1−22=0\frac{i \cos{\left(p \right)} \left(x + 1\right)}{4} - 1 - \frac{\sqrt{2}}{2} = 0
Sustituimos
w=cos⁡(p)w = \cos{\left(p \right)}
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 - sqrt2/2 + i*wx/4+1/4 = 0

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-1 - sqrt(2)/2 + i*w*(1 + x)/4 = 0

Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
iw(x+1)4−22=1\frac{i w \left(x + 1\right)}{4} - \frac{\sqrt{2}}{2} = 1
Dividamos ambos miembros de la ecuación en (-sqrt(2)/2 + i*w*(1 + x)/4)/w
w = 1 / ((-sqrt(2)/2 + i*w*(1 + x)/4)/w)

Obtenemos la respuesta: w = -2*i*(2 + sqrt(2))/(1 + x)
hacemos cambio inverso
cos⁡(p)=w\cos{\left(p \right)} = w
sustituimos w:
Gráfica
Suma y producto de raíces [src] 
suma
                    ___                                                    ___                                
                2*\/ 2 *sin(re(p))*sinh(im(p))                       2*I*\/ 2 *cos(re(p))*cosh(im(p))         
-1 + --------------------------------------------------- - ---------------------------------------------------
        2            2             2            2             2            2             2            2       
     cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))   cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
−1+22sin⁡(re⁡(p))sinh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))−22icos⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))-1 + \frac{2 \sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{2 \sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} 
=
                    ___                                                    ___                                
                2*\/ 2 *sin(re(p))*sinh(im(p))                       2*I*\/ 2 *cos(re(p))*cosh(im(p))         
-1 + --------------------------------------------------- - ---------------------------------------------------
        2            2             2            2             2            2             2            2       
     cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))   cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
−1+22sin⁡(re⁡(p))sinh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))−22icos⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))-1 + \frac{2 \sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{2 \sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} 
producto
                    ___                                                    ___                                
                2*\/ 2 *sin(re(p))*sinh(im(p))                       2*I*\/ 2 *cos(re(p))*cosh(im(p))         
-1 + --------------------------------------------------- - ---------------------------------------------------
        2            2             2            2             2            2             2            2       
     cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))   cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
−1+22sin⁡(re⁡(p))sinh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))−22icos⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))-1 + \frac{2 \sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{2 \sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} 
=
 /  /      ___                         \                         \ 
-\I*\- 2*\/ 2  + sin(re(p))*sinh(im(p))/ - cos(re(p))*cosh(im(p))/ 
-------------------------------------------------------------------
         -cos(re(p))*cosh(im(p)) + I*sin(re(p))*sinh(im(p))
−i(sin⁡(re⁡(p))sinh⁡(im⁡(p))−22)−cos⁡(re⁡(p))cosh⁡(im⁡(p))isin⁡(re⁡(p))sinh⁡(im⁡(p))−cos⁡(re⁡(p))cosh⁡(im⁡(p))- \frac{i \left(\sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - 2 \sqrt{2}\right) - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}} 
-(i*(-2*sqrt(2) + sin(re(p))*sinh(im(p))) - cos(re(p))*cosh(im(p)))/(-cos(re(p))*cosh(im(p)) + i*sin(re(p))*sinh(im(p)))
Respuesta rápida [src] 
                         ___                                                    ___                                
                     2*\/ 2 *sin(re(p))*sinh(im(p))                       2*I*\/ 2 *cos(re(p))*cosh(im(p))         
x1 = -1 + --------------------------------------------------- - ---------------------------------------------------
             2            2             2            2             2            2             2            2       
          cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))   cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
x1=−1+22sin⁡(re⁡(p))sinh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))−22icos⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡2(re⁡(p))sinh⁡2(im⁡(p))+cos⁡2(re⁡(p))cosh⁡2(im⁡(p))x_{1} = -1 + \frac{2 \sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{2 \sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} 
x1 = -1 + 2*sqrt(2)*sin(re(p))*sinh(im(p))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2) - 2*sqrt(2)*i*cos(re(p))*cosh(im(p))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2)
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