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sin2xcos2x+2cos2xsinxcosx-sin2xsin^2x=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                                                           2       
sin(2*x)*cos(2*x) + 2*cos(2*x)*sin(x)*cos(x) - sin(2*x)*sin (x) = 0
$$\left(\sin{\left(x \right)} 2 \cos{\left(2 x \right)} \cos{\left(x \right)} + \sin{\left(2 x \right)} \cos{\left(2 x \right)}\right) - \sin^{2}{\left(x \right)} \sin{\left(2 x \right)} = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 0
$$x_{1} = 0$$ 
     -pi 
x2 = ----
      2
$$x_{2} = - \frac{\pi}{2}$$ 
     pi
x3 = --
     2
$$x_{3} = \frac{\pi}{2}$$ 
x4 = pi
$$x_{4} = \pi$$ 
              /   /    /    ___\\\                          
              |   |atan\2*\/ 6 /||                          
              |sin|-------------||                          
              |   \      2      /|     /log(5)      /  ___\\
x5 = pi - atan|------------------| + I*|------ - log\\/ 5 /|
              |   /    /    ___\\|     \  2                /
              |   |atan\2*\/ 6 /||                          
              |cos|-------------||                          
              \   \      2      //
$$x_{5} = - \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \sqrt{6} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \sqrt{6} \right)}}{2} \right)}} \right)} + \pi + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$ 
                                         /   /    /    ___\\\
                                         |   |atan\2*\/ 6 /||
                                         |sin|-------------||
             /log(5)      /  ___\\       |   \      2      /|
x6 = -pi + I*|------ - log\\/ 5 /| + atan|------------------|
             \  2                /       |   /    /    ___\\|
                                         |   |atan\2*\/ 6 /||
                                         |cos|-------------||
                                         \   \      2      //
$$x_{6} = - \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \sqrt{6} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \sqrt{6} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$ 
       /     /          ___\         \
     I*\- log\1 - 2*I*\/ 6 / + log(5)/
x7 = ---------------------------------
                     2
$$x_{7} = \frac{i \left(\log{\left(5 \right)} - \log{\left(1 - 2 \sqrt{6} i \right)}\right)}{2}$$ 
       /     /          ___\         \
     I*\- log\1 + 2*I*\/ 6 / + log(5)/
x8 = ---------------------------------
                     2
$$x_{8} = \frac{i \left(\log{\left(5 \right)} - \log{\left(1 + 2 \sqrt{6} i \right)}\right)}{2}$$ 
x8 = i*(log(5) - log(1 + 2*sqrt(6)*i))/2
Suma y producto de raíces [src] 
suma
                          /   /    /    ___\\\                                                                 /   /    /    ___\\\                                                                        
                          |   |atan\2*\/ 6 /||                                                                 |   |atan\2*\/ 6 /||                                                                        
                          |sin|-------------||                                                                 |sin|-------------||     /     /          ___\         \     /     /          ___\         \
  pi   pi                 |   \      2      /|     /log(5)      /  ___\\           /log(5)      /  ___\\       |   \      2      /|   I*\- log\1 - 2*I*\/ 6 / + log(5)/   I*\- log\1 + 2*I*\/ 6 / + log(5)/
- -- + -- + pi + pi - atan|------------------| + I*|------ - log\\/ 5 /| + -pi + I*|------ - log\\/ 5 /| + atan|------------------| + --------------------------------- + ---------------------------------
  2    2                  |   /    /    ___\\|     \  2                /           \  2                /       |   /    /    ___\\|                   2                                   2                
                          |   |atan\2*\/ 6 /||                                                                 |   |atan\2*\/ 6 /||                                                                        
                          |cos|-------------||                                                                 |cos|-------------||                                                                        
                          \   \      2      //                                                                 \   \      2      //
$$\frac{i \left(\log{\left(5 \right)} - \log{\left(1 + 2 \sqrt{6} i \right)}\right)}{2} + \left(\frac{i \left(\log{\left(5 \right)} - \log{\left(1 - 2 \sqrt{6} i \right)}\right)}{2} + \left(\left(\left(\left(- \frac{\pi}{2} + \frac{\pi}{2}\right) + \pi\right) + \left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \sqrt{6} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \sqrt{6} \right)}}{2} \right)}} \right)} + \pi + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right) + \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \sqrt{6} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \sqrt{6} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right)\right)$$ 
=
       /     /          ___\         \     /     /          ___\         \                            
     I*\- log\1 - 2*I*\/ 6 / + log(5)/   I*\- log\1 + 2*I*\/ 6 / + log(5)/       /log(5)      /  ___\\
pi + --------------------------------- + --------------------------------- + 2*I*|------ - log\\/ 5 /|
                     2                                   2                       \  2                /
$$\pi + \frac{i \left(\log{\left(5 \right)} - \log{\left(1 - 2 \sqrt{6} i \right)}\right)}{2} + \frac{i \left(\log{\left(5 \right)} - \log{\left(1 + 2 \sqrt{6} i \right)}\right)}{2} + 2 i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$ 
producto
             /         /   /    /    ___\\\                          \ /                                    /   /    /    ___\\\\                                                                    
             |         |   |atan\2*\/ 6 /||                          | |                                    |   |atan\2*\/ 6 /|||                                                                    
             |         |sin|-------------||                          | |                                    |sin|-------------|||   /     /          ___\         \   /     /          ___\         \
  -pi  pi    |         |   \      2      /|     /log(5)      /  ___\\| |        /log(5)      /  ___\\       |   \      2      /|| I*\- log\1 - 2*I*\/ 6 / + log(5)/ I*\- log\1 + 2*I*\/ 6 / + log(5)/
0*----*--*pi*|pi - atan|------------------| + I*|------ - log\\/ 5 /||*|-pi + I*|------ - log\\/ 5 /| + atan|------------------||*---------------------------------*---------------------------------
   2   2     |         |   /    /    ___\\|     \  2                /| |        \  2                /       |   /    /    ___\\||                 2                                 2                
             |         |   |atan\2*\/ 6 /||                          | |                                    |   |atan\2*\/ 6 /|||                                                                    
             |         |cos|-------------||                          | |                                    |cos|-------------|||                                                                    
             \         \   \      2      //                          / \                                    \   \      2      ///
$$\frac{i \left(\log{\left(5 \right)} - \log{\left(1 + 2 \sqrt{6} i \right)}\right)}{2} \frac{i \left(\log{\left(5 \right)} - \log{\left(1 - 2 \sqrt{6} i \right)}\right)}{2} \pi \frac{\pi}{2} \cdot 0 \left(- \frac{\pi}{2}\right) \left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \sqrt{6} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \sqrt{6} \right)}}{2} \right)}} \right)} + \pi + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \sqrt{6} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \sqrt{6} \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)$$ 
=
0
$$0$$ 
0
Respuesta numérica [src] 
x1 = -43.9822971502571
x2 = -29.845130209103
x3 = -19.534275124541
x4 = -69.7997575819777
x5 = 69.7997575819777
x6 = 33.8727999864854
x7 = -18.1648367185365
x8 = -92.6769832808989
x9 = -54.0917943140288
x10 = 16.3926824709513
x11 = -99.8462457118711
x12 = 28.2743338823081
x13 = 29.845130209103
x14 = -81.6814089933346
x15 = 99.8462457118711
x16 = -15.707963267949
x17 = 72.2566310325652
x18 = 55.863948561614
x19 = 95.8185759344887
x20 = 40.155985293665
x21 = -47.8086090068492
x22 = -76.0829428891573
x23 = -10.1094971637717
x24 = -21.9911485751286
x25 = -14.1371669411541
x26 = 82.3661281963369
x27 = 98.0740914642859
x28 = 42.4115008234622
x29 = 24.4480220257161
x30 = 68.4303191759732
x31 = 3.82631185659208
x32 = 38.3838310460798
x33 = 46.4391706008446
x34 = 50.2654824574367
x35 = -63.5165722747982
x36 = -40.155985293665
x37 = -72.9413502355675
x38 = -48.6946861306418
x39 = 10.1094971637717
x40 = 54.0917943140288
x41 = -62.1471338687936
x42 = -80.1106126665397
x43 = -27.5896146793059
x44 = -87.9645943005142
x45 = -85.5077208499267
x46 = 0.0
x47 = 20.4203522483337
x48 = 90.4214677511017
x49 = -65.9734457253857
x50 = -73.8274273593601
x51 = -84.1382824439221
x52 = -11.8816514113569
x53 = 6.28318530717959
x54 = -67.5442420521806
x55 = -36.1283155162826
x56 = 94.2477796076938
x57 = 65.9734457253857
x58 = 36.1283155162826
x59 = 21.9911485751286
x60 = -89.5353906273091
x61 = -41.5254236996696
x62 = 91.7909061571063
x63 = 7.85398163397448
x64 = 14.1371669411541
x65 = 86.3937979737193
x66 = 87.9645943005142
x67 = 11.8816514113569
x68 = -32.1006457389002
x69 = -55.863948561614
x70 = -3.82631185659208
x71 = 77.8550971367425
x72 = 51.8362787842316
x73 = -37.6991118430775
x74 = 25.8174604317206
x75 = -51.8362787842316
x76 = -1.5707963267949
x77 = -23.5619449019235
x78 = 64.4026493985908
x79 = 43.9822971502571
x80 = 32.1006457389002
x81 = 76.0829428891573
x82 = -95.8185759344887
x83 = -98.0740914642859
x84 = 80.1106126665397
x85 = 73.8274273593601
x86 = 47.8086090068492
x87 = -59.6902604182061
x88 = 62.1471338687936
x89 = -7.85398163397448
x90 = -77.8550971367425
x91 = -91.7909061571063
x92 = -25.8174604317206
x93 = 84.1382824439221
x94 = -33.8727999864854
x95 = 18.1648367185365
x96 = 60.3749796212084
x97 = -45.553093477052
x98 = 2.45687345058751
x99 = -58.1194640914112
x100 = -5.5984661041773
x101 = 58.1194640914112
x101 = 58.1194640914112
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