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(1+2*(cos(x)+sin(x))^2/(-cos(x)+sin(x))^2)/(-cos(x)+sin(x))=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                       2    
    2*(cos(x) + sin(x))     
1 + --------------------    
                      2     
    (-cos(x) + sin(x))      
------------------------ = 0
    -cos(x) + sin(x)
1+2(sin⁡(x)+cos⁡(x))2(sin⁡(x)−cos⁡(x))2sin⁡(x)−cos⁡(x)=0\frac{1 + \frac{2 \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}}{\left(\sin{\left(x \right)} - \cos{\left(x \right)}\right)^{2}}}{\sin{\left(x \right)} - \cos{\left(x \right)}} = 0
Simplificar
Gráfica
0-80-60-40-2020406080-100100-5000000000050000000000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
           /    /        ___\\         /    /        ___\\
           |    |1   I*\/ 2 ||         |    |1   I*\/ 2 ||
x1 = - 2*re|atan|- - -------|| - 2*I*im|atan|- - -------||
           \    \3      3   //         \    \3      3   //
x1=−2re⁡(atan⁡(13−2i3))−2iim⁡(atan⁡(13−2i3))x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} 
           /    /        ___\\         /    /        ___\\
           |    |1   I*\/ 2 ||         |    |1   I*\/ 2 ||
x2 = - 2*re|atan|- + -------|| - 2*I*im|atan|- + -------||
           \    \3      3   //         \    \3      3   //
x2=−2re⁡(atan⁡(13+2i3))−2iim⁡(atan⁡(13+2i3))x_{2} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} 
         /    /        ___\\         /    /        ___\\
x3 = 2*re\atan\1 - I*\/ 2 // + 2*I*im\atan\1 - I*\/ 2 //
x3=2re⁡(atan⁡(1−2i))+2iim⁡(atan⁡(1−2i))x_{3} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} 
         /    /        ___\\         /    /        ___\\
x4 = 2*re\atan\1 + I*\/ 2 // + 2*I*im\atan\1 + I*\/ 2 //
x4=2re⁡(atan⁡(1+2i))+2iim⁡(atan⁡(1+2i))x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} 
x4 = 2*re(atan(1 + sqrt(2)*i)) + 2*i*im(atan(1 + sqrt(2)*i))
Suma y producto de raíces [src] 
suma
      /    /        ___\\         /    /        ___\\         /    /        ___\\         /    /        ___\\                                                                                                            
      |    |1   I*\/ 2 ||         |    |1   I*\/ 2 ||         |    |1   I*\/ 2 ||         |    |1   I*\/ 2 ||       /    /        ___\\         /    /        ___\\       /    /        ___\\         /    /        ___\\
- 2*re|atan|- - -------|| - 2*I*im|atan|- - -------|| + - 2*re|atan|- + -------|| - 2*I*im|atan|- + -------|| + 2*re\atan\1 - I*\/ 2 // + 2*I*im\atan\1 - I*\/ 2 // + 2*re\atan\1 + I*\/ 2 // + 2*I*im\atan\1 + I*\/ 2 //
      \    \3      3   //         \    \3      3   //         \    \3      3   //         \    \3      3   //
(((−2re⁡(atan⁡(13+2i3))−2iim⁡(atan⁡(13+2i3)))+(−2re⁡(atan⁡(13−2i3))−2iim⁡(atan⁡(13−2i3))))+(2re⁡(atan⁡(1−2i))+2iim⁡(atan⁡(1−2i))))+(2re⁡(atan⁡(1+2i))+2iim⁡(atan⁡(1+2i)))\left(\left(\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right) 
=
      /    /        ___\\       /    /        ___\\                                                             /    /        ___\\         /    /        ___\\                                                        
      |    |1   I*\/ 2 ||       |    |1   I*\/ 2 ||       /    /        ___\\       /    /        ___\\         |    |1   I*\/ 2 ||         |    |1   I*\/ 2 ||         /    /        ___\\         /    /        ___\\
- 2*re|atan|- - -------|| - 2*re|atan|- + -------|| + 2*re\atan\1 + I*\/ 2 // + 2*re\atan\1 - I*\/ 2 // - 2*I*im|atan|- - -------|| - 2*I*im|atan|- + -------|| + 2*I*im\atan\1 + I*\/ 2 // + 2*I*im\atan\1 - I*\/ 2 //
      \    \3      3   //       \    \3      3   //                                                             \    \3      3   //         \    \3      3   //
−2re⁡(atan⁡(13−2i3))−2re⁡(atan⁡(13+2i3))+2re⁡(atan⁡(1+2i))+2re⁡(atan⁡(1−2i))−2iim⁡(atan⁡(13+2i3))+2iim⁡(atan⁡(1−2i))−2iim⁡(atan⁡(13−2i3))+2iim⁡(atan⁡(1+2i))- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} 
producto
/      /    /        ___\\         /    /        ___\\\ /      /    /        ___\\         /    /        ___\\\                                                                                                            
|      |    |1   I*\/ 2 ||         |    |1   I*\/ 2 ||| |      |    |1   I*\/ 2 ||         |    |1   I*\/ 2 ||| /    /    /        ___\\         /    /        ___\\\ /    /    /        ___\\         /    /        ___\\\
|- 2*re|atan|- - -------|| - 2*I*im|atan|- - -------|||*|- 2*re|atan|- + -------|| - 2*I*im|atan|- + -------|||*\2*re\atan\1 - I*\/ 2 // + 2*I*im\atan\1 - I*\/ 2 ///*\2*re\atan\1 + I*\/ 2 // + 2*I*im\atan\1 + I*\/ 2 ///
\      \    \3      3   //         \    \3      3   /// \      \    \3      3   //         \    \3      3   ///
(−2re⁡(atan⁡(13−2i3))−2iim⁡(atan⁡(13−2i3)))(−2re⁡(atan⁡(13+2i3))−2iim⁡(atan⁡(13+2i3)))(2re⁡(atan⁡(1−2i))+2iim⁡(atan⁡(1−2i)))(2re⁡(atan⁡(1+2i))+2iim⁡(atan⁡(1+2i)))\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right) 
=
                                                                                                       /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\
   /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\ |    |    |1   I*\/ 2 ||     |    |1   I*\/ 2 ||| |    |    |1   I*\/ 2 ||     |    |1   I*\/ 2 |||
16*\I*im\atan\1 + I*\/ 2 // + re\atan\1 + I*\/ 2 ///*\I*im\atan\1 - I*\/ 2 // + re\atan\1 - I*\/ 2 ///*|I*im|atan|- - -------|| + re|atan|- - -------|||*|I*im|atan|- + -------|| + re|atan|- + -------|||
                                                                                                       \    \    \3      3   //     \    \3      3   /// \    \    \3      3   //     \    \3      3   ///
16(re⁡(atan⁡(13−2i3))+iim⁡(atan⁡(13−2i3)))(re⁡(atan⁡(13+2i3))+iim⁡(atan⁡(13+2i3)))(re⁡(atan⁡(1−2i))+iim⁡(atan⁡(1−2i)))(re⁡(atan⁡(1+2i))+iim⁡(atan⁡(1+2i)))16 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{2} i}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{2} i}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right) 
16*(i*im(atan(1 + i*sqrt(2))) + re(atan(1 + i*sqrt(2))))*(i*im(atan(1 - i*sqrt(2))) + re(atan(1 - i*sqrt(2))))*(i*im(atan(1/3 - i*sqrt(2)/3)) + re(atan(1/3 - i*sqrt(2)/3)))*(i*im(atan(1/3 + i*sqrt(2)/3)) + re(atan(1/3 + i*sqrt(2)/3)))
Respuesta numérica [src] 
x1 = -0.785398163397448 + 0.881373587019543*i
x2 = -0.785398163397448 - 0.881373587019543*i
x3 = 2.35619449019234 - 0.881373587019543*i
x4 = 2.35619449019234 + 0.881373587019543*i
x4 = 2.35619449019234 + 0.881373587019543*i
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