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1+(sin(x))^2=sin(2*x) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
       2              
1 + sin (x) = sin(2*x)
sin⁡2(x)+1=sin⁡(2x)\sin^{2}{\left(x \right)} + 1 = \sin{\left(2 x \right)}
Simplificar
Gráfica
0-80-60-40-2020406080-1001005-5
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
                                         /   /atan(2)\\
                                         |sin|-------||
             /log(5)      /4 ___\\       |   \   2   /|
x1 = -pi + I*|------ - log\\/ 5 /| + atan|------------|
             \  2                /       |   /atan(2)\|
                                         |cos|-------||
                                         \   \   2   //
x1=−π+atan⁡(sin⁡(atan⁡(2)2)cos⁡(atan⁡(2)2))+i(−log⁡(54)+log⁡(5)2)x_{1} = - \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right) 
                 /            /  ___\\
     atan(2)     |log(5)   log\\/ 5 /|
x2 = ------- + I*|------ - ----------|
        2        \  2          2     /
x2=atan⁡(2)2+i(−log⁡(5)2+log⁡(5)2)x_{2} = \frac{\operatorname{atan}{\left(2 \right)}}{2} + i \left(- \frac{\log{\left(\sqrt{5} \right)}}{2} + \frac{\log{\left(5 \right)}}{2}\right) 
                              /   /atan(2)\\
                              |sin|-------||
                /4 ___\       |   \   2   /|
x3 = -pi - I*log\\/ 5 / + atan|------------|
                              |   /atan(2)\|
                              |cos|-------||
                              \   \   2   //
x3=−π+atan⁡(sin⁡(atan⁡(2)2)cos⁡(atan⁡(2)2))−ilog⁡(54)x_{3} = - \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} - i \log{\left(\sqrt[4]{5} \right)} 
                    /  ___\
     atan(2)   I*log\\/ 5 /
x4 = ------- - ------------
        2           2
x4=atan⁡(2)2−ilog⁡(5)2x_{4} = \frac{\operatorname{atan}{\left(2 \right)}}{2} - \frac{i \log{\left(\sqrt{5} \right)}}{2} 
x4 = atan(2)/2 - i*log(sqrt(5))/2
Suma y producto de raíces [src] 
suma
                                    /   /atan(2)\\                                                                /   /atan(2)\\                         
                                    |sin|-------||               /            /  ___\\                            |sin|-------||                  /  ___\
        /log(5)      /4 ___\\       |   \   2   /|   atan(2)     |log(5)   log\\/ 5 /|              /4 ___\       |   \   2   /|   atan(2)   I*log\\/ 5 /
-pi + I*|------ - log\\/ 5 /| + atan|------------| + ------- + I*|------ - ----------| + -pi - I*log\\/ 5 / + atan|------------| + ------- - ------------
        \  2                /       |   /atan(2)\|      2        \  2          2     /                            |   /atan(2)\|      2           2      
                                    |cos|-------||                                                                |cos|-------||                         
                                    \   \   2   //                                                                \   \   2   //
(atan⁡(2)2−ilog⁡(5)2)+((−π+atan⁡(sin⁡(atan⁡(2)2)cos⁡(atan⁡(2)2))−ilog⁡(54))+((−π+atan⁡(sin⁡(atan⁡(2)2)cos⁡(atan⁡(2)2))+i(−log⁡(54)+log⁡(5)2))+(atan⁡(2)2+i(−log⁡(5)2+log⁡(5)2))))\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} - \frac{i \log{\left(\sqrt{5} \right)}}{2}\right) + \left(\left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} - i \log{\left(\sqrt[4]{5} \right)}\right) + \left(\left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) + \left(\frac{\operatorname{atan}{\left(2 \right)}}{2} + i \left(- \frac{\log{\left(\sqrt{5} \right)}}{2} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right)\right) 
=
              /   /atan(2)\\                                                                                            
              |sin|-------||                               /            /  ___\\                       /  ___\          
              |   \   2   /|     /log(5)      /4 ___\\     |log(5)   log\\/ 5 /|        /4 ___\   I*log\\/ 5 /          
-2*pi + 2*atan|------------| + I*|------ - log\\/ 5 /| + I*|------ - ----------| - I*log\\/ 5 / - ------------ + atan(2)
              |   /atan(2)\|     \  2                /     \  2          2     /                       2                
              |cos|-------||                                                                                            
              \   \   2   //
−2π+2atan⁡(sin⁡(atan⁡(2)2)cos⁡(atan⁡(2)2))+atan⁡(2)−ilog⁡(54)−ilog⁡(5)2+i(−log⁡(54)+log⁡(5)2)+i(−log⁡(5)2+log⁡(5)2)- 2 \pi + 2 \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} + \operatorname{atan}{\left(2 \right)} - i \log{\left(\sqrt[4]{5} \right)} - \frac{i \log{\left(\sqrt{5} \right)}}{2} + i \left(- \log{\left(\sqrt[4]{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right) + i \left(- \frac{\log{\left(\sqrt{5} \right)}}{2} + \frac{\log{\left(5 \right)}}{2}\right) 
producto
/                                    /   /atan(2)\\\                                     /                         /   /atan(2)\\\                         
|                                    |sin|-------||| /            /            /  ___\\\ |                         |sin|-------||| /               /  ___\\
|        /log(5)      /4 ___\\       |   \   2   /|| |atan(2)     |log(5)   log\\/ 5 /|| |           /4 ___\       |   \   2   /|| |atan(2)   I*log\\/ 5 /|
|-pi + I*|------ - log\\/ 5 /| + atan|------------||*|------- + I*|------ - ----------||*|-pi - I*log\\/ 5 / + atan|------------||*|------- - ------------|
|        \  2                /       |   /atan(2)\|| \   2        \  2          2     // |                         |   /atan(2)\|| \   2           2      /
|                                    |cos|-------|||                                     |                         |cos|-------|||                         
\                                    \   \   2   ///                                     \                         \   \   2   ///
(atan⁡(2)2+i(−log⁡(5)2+log⁡(5)2))(−π+atan⁡(sin⁡(atan⁡(2)2)cos⁡(atan⁡(2)2))+i(−log⁡(54)+log⁡(5)2))(−π+atan⁡(sin⁡(atan⁡(2)2)cos⁡(atan⁡(2)2))−ilog⁡(54))(atan⁡(2)2−ilog⁡(5)2)\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} + i \left(- \frac{\log{\left(\sqrt{5} \right)}}{2} + \frac{\log{\left(5 \right)}}{2}\right)\right) \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} - i \log{\left(\sqrt[4]{5} \right)}\right) \left(\frac{\operatorname{atan}{\left(2 \right)}}{2} - \frac{i \log{\left(\sqrt{5} \right)}}{2}\right) 
=
    4         4             3        2     2        2    2          2       2            2           
atan (2)   log (5)   pi*atan (2)   pi *atan (2)   pi *log (5)   atan (2)*log (5)   pi*log (5)*atan(2)
-------- + ------- - ----------- + ------------ + ----------- + ---------------- - ------------------
   16        256          4             4              16              32                  16
−πatan⁡3(2)4−πlog⁡(5)2atan⁡(2)16+log⁡(5)4256+atan⁡4(2)16+log⁡(5)2atan⁡2(2)32+π2log⁡(5)216+π2atan⁡2(2)4- \frac{\pi \operatorname{atan}^{3}{\left(2 \right)}}{4} - \frac{\pi \log{\left(5 \right)}^{2} \operatorname{atan}{\left(2 \right)}}{16} + \frac{\log{\left(5 \right)}^{4}}{256} + \frac{\operatorname{atan}^{4}{\left(2 \right)}}{16} + \frac{\log{\left(5 \right)}^{2} \operatorname{atan}^{2}{\left(2 \right)}}{32} + \frac{\pi^{2} \log{\left(5 \right)}^{2}}{16} + \frac{\pi^{2} \operatorname{atan}^{2}{\left(2 \right)}}{4} 
atan(2)^4/16 + log(5)^4/256 - pi*atan(2)^3/4 + pi^2*atan(2)^2/4 + pi^2*log(5)^2/16 + atan(2)^2*log(5)^2/32 - pi*log(5)^2*atan(2)/16
Respuesta numérica [src] 
x1 = -2.58801829469275 + 0.402359478108525*i
x2 = 0.553574358897045 + 0.402359478108525*i
x3 = -2.58801829469275 - 0.402359478108525*i
x4 = 0.553574358897045 - 0.402359478108525*i
x4 = 0.553574358897045 - 0.402359478108525*i
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