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(2cosx/2-sqrt2)*(sin5x+2)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
/2*cos(x)     ___\                   
|-------- - \/ 2 |*(sin(5*x) + 2) = 0
\   2            /
(2cos⁡(x)2−2)(sin⁡(5x)+2)=0\left(\frac{2 \cos{\left(x \right)}}{2} - \sqrt{2}\right) \left(\sin{\left(5 x \right)} + 2\right) = 0
Simplificar
Gráfica
0-80-60-40-2020406080-100100-1010
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
           /    /        ___\\         /    /        ___\\
           |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
       2*re|atan|- - -------||   2*I*im|atan|- - -------||
           \    \2      2   //         \    \2      2   //
x1 = - ----------------------- - -------------------------
                  5                          5
x1=−2re⁡(atan⁡(12−3i2))5−2iim⁡(atan⁡(12−3i2))5x_{1} = - \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} 
           /    /        ___\\         /    /        ___\\
           |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
       2*re|atan|- + -------||   2*I*im|atan|- + -------||
           \    \2      2   //         \    \2      2   //
x2 = - ----------------------- - -------------------------
                  5                          5
x2=−2re⁡(atan⁡(12+3i2))5−2iim⁡(atan⁡(12+3i2))5x_{2} = - \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} 
               /   ____________\
               |  /        ___ |
               |\/  -1 + \/ 2  |
x3 = -2*I*atanh|---------------|
               |    ___________|
               |   /       ___ |
               \ \/  1 + \/ 2  /
x3=−2iatanh⁡(−1+21+2)x_{3} = - 2 i \operatorname{atanh}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)} 
              /   ____________\
              |  /        ___ |
              |\/  -1 + \/ 2  |
x4 = 2*I*atanh|---------------|
              |    ___________|
              |   /       ___ |
              \ \/  1 + \/ 2  /
x4=2iatanh⁡(−1+21+2)x_{4} = 2 i \operatorname{atanh}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)} 
x4 = 2*i*atanh(sqrt(-1 + sqrt(2))/sqrt(1 + sqrt(2)))
Suma y producto de raíces [src] 
suma
      /    /        ___\\         /    /        ___\\         /    /        ___\\         /    /        ___\\                                                          
      |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||            /   ____________\            /   ____________\
  2*re|atan|- - -------||   2*I*im|atan|- - -------||     2*re|atan|- + -------||   2*I*im|atan|- + -------||            |  /        ___ |            |  /        ___ |
      \    \2      2   //         \    \2      2   //         \    \2      2   //         \    \2      2   //            |\/  -1 + \/ 2  |            |\/  -1 + \/ 2  |
- ----------------------- - ------------------------- + - ----------------------- - ------------------------- - 2*I*atanh|---------------| + 2*I*atanh|---------------|
             5                          5                            5                          5                        |    ___________|            |    ___________|
                                                                                                                         |   /       ___ |            |   /       ___ |
                                                                                                                         \ \/  1 + \/ 2  /            \ \/  1 + \/ 2  /
(((−2re⁡(atan⁡(12+3i2))5−2iim⁡(atan⁡(12+3i2))5)+(−2re⁡(atan⁡(12−3i2))5−2iim⁡(atan⁡(12−3i2))5))−2iatanh⁡(−1+21+2))+2iatanh⁡(−1+21+2)\left(\left(\left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5}\right) + \left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5}\right)\right) - 2 i \operatorname{atanh}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)}\right) + 2 i \operatorname{atanh}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)} 
=
      /    /        ___\\       /    /        ___\\         /    /        ___\\         /    /        ___\\
      |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||
  2*re|atan|- + -------||   2*re|atan|- - -------||   2*I*im|atan|- + -------||   2*I*im|atan|- - -------||
      \    \2      2   //       \    \2      2   //         \    \2      2   //         \    \2      2   //
- ----------------------- - ----------------------- - ------------------------- - -------------------------
             5                         5                          5                           5
−2re⁡(atan⁡(12+3i2))5−2re⁡(atan⁡(12−3i2))5−2iim⁡(atan⁡(12+3i2))5−2iim⁡(atan⁡(12−3i2))5- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} 
producto
/      /    /        ___\\         /    /        ___\\\ /      /    /        ___\\         /    /        ___\\\                                                       
|      |    |1   I*\/ 3 ||         |    |1   I*\/ 3 ||| |      |    |1   I*\/ 3 ||         |    |1   I*\/ 3 |||           /   ____________\          /   ____________\
|  2*re|atan|- - -------||   2*I*im|atan|- - -------||| |  2*re|atan|- + -------||   2*I*im|atan|- + -------|||           |  /        ___ |          |  /        ___ |
|      \    \2      2   //         \    \2      2   //| |      \    \2      2   //         \    \2      2   //|           |\/  -1 + \/ 2  |          |\/  -1 + \/ 2  |
|- ----------------------- - -------------------------|*|- ----------------------- - -------------------------|*-2*I*atanh|---------------|*2*I*atanh|---------------|
\             5                          5            / \             5                          5            /           |    ___________|          |    ___________|
                                                                                                                          |   /       ___ |          |   /       ___ |
                                                                                                                          \ \/  1 + \/ 2  /          \ \/  1 + \/ 2  /
2iatanh⁡(−1+21+2)−2iatanh⁡(−1+21+2)(−2re⁡(atan⁡(12−3i2))5−2iim⁡(atan⁡(12−3i2))5)(−2re⁡(atan⁡(12+3i2))5−2iim⁡(atan⁡(12+3i2))5)2 i \operatorname{atanh}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)} - 2 i \operatorname{atanh}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)} \left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}}{5}\right) \left(- \frac{2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5} - \frac{2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}}{5}\right) 
=
         /   ____________\                                                                                                    
         |  /        ___ | /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\
        2|\/  -1 + \/ 2  | |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 ||| |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 |||
16*atanh |---------------|*|I*im|atan|- + -------|| + re|atan|- + -------|||*|I*im|atan|- - -------|| + re|atan|- - -------|||
         |    ___________| \    \    \2      2   //     \    \2      2   /// \    \    \2      2   //     \    \2      2   ///
         |   /       ___ |                                                                                                    
         \ \/  1 + \/ 2  /                                                                                                    
------------------------------------------------------------------------------------------------------------------------------
                                                              25
16(re⁡(atan⁡(12−3i2))+iim⁡(atan⁡(12−3i2)))(re⁡(atan⁡(12+3i2))+iim⁡(atan⁡(12+3i2)))atanh⁡2(−1+21+2)25\frac{16 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right) \operatorname{atanh}^{2}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)}}{25} 
16*atanh(sqrt(-1 + sqrt(2))/sqrt(1 + sqrt(2)))^2*(i*im(atan(1/2 + i*sqrt(3)/2)) + re(atan(1/2 + i*sqrt(3)/2)))*(i*im(atan(1/2 - i*sqrt(3)/2)) + re(atan(1/2 - i*sqrt(3)/2)))/25
Respuesta numérica [src] 
x1 = -0.881373587019543*i
x2 = 0.881373587019543*i
x3 = -0.314159265358979 + 0.263391579384963*i
x4 = -0.314159265358979 - 0.263391579384963*i
x4 = -0.314159265358979 - 0.263391579384963*i
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