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tg2x(1/cos^2x-3-tgx)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
         /   1                \    
tan(2*x)*|------- - 3 - tan(x)| = 0
         |   2                |    
         \cos (x)             /
$$\left(\left(-3 + \frac{1}{\cos^{2}{\left(x \right)}}\right) - \tan{\left(x \right)}\right) \tan{\left(2 x \right)} = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
             /log(5)      /  ___\\               /log(5)      /  ___\\                  /    5/2\
pi + -pi + I*|------ - log\\/ 5 /| + atan(2) + I*|------ - log\\/ 5 /| + atan(2) - I*log\(-I)   /
             \  2                /               \  2                /
$$- i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} + \left(\left(\pi + \left(- \pi + \operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right)$$ 
=
                 /    5/2\       /log(5)      /  ___\\
2*atan(2) - I*log\(-I)   / + 2*I*|------ - log\\/ 5 /|
                                 \  2                /
$$2 \operatorname{atan}{\left(2 \right)} - i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} + 2 i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$ 
producto
     /        /log(5)      /  ___\\          \ /  /log(5)      /  ___\\          \ /      /    5/2\\
0*pi*|-pi + I*|------ - log\\/ 5 /| + atan(2)|*|I*|------ - log\\/ 5 /| + atan(2)|*\-I*log\(-I)   //
     \        \  2                /          / \  \  2                /          /
$$- i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} 0 \pi \left(- \pi + \operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)$$ 
=
0
$$0$$ 
0
Respuesta rápida [src] 
x1 = 0
$$x_{1} = 0$$ 
x2 = pi
$$x_{2} = \pi$$ 
             /log(5)      /  ___\\          
x3 = -pi + I*|------ - log\\/ 5 /| + atan(2)
             \  2                /
$$x_{3} = - \pi + \operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$ 
       /log(5)      /  ___\\          
x4 = I*|------ - log\\/ 5 /| + atan(2)
       \  2                /
$$x_{4} = \operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$ 
           /    5/2\
x5 = -I*log\(-I)   /
$$x_{5} = - i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)}$$ 
x5 = -i*log((-i)^(5/2))
Respuesta numérica [src] 
x1 = 12.5663706143592
x2 = 78.5398163397448
x3 = 70.2221870967695
x4 = -65.9734457253857
x5 = -15.707963267949
x6 = -34.5575191894877
x7 = -69.1150383789755
x8 = 50.2654824574367
x9 = 81.6814089933346
x10 = 3.14159265358979
x11 = -56.5486677646163
x12 = -25.1327412287183
x13 = -46.0167410860528
x14 = -100.530964914873
x15 = -91.106186954104
x16 = 18.8495559215388
x17 = -75.398223686155
x18 = 56.5486677646163
x19 = 75.398223686155
x20 = -24.0255925109243
x21 = -17.7424072037447
x22 = 15.707963267949
x23 = -83.7158529291303
x24 = -59.6902604182061
x25 = 21.9911485751286
x26 = 6.28318530717959
x27 = 69.1150383789755
x28 = 62.8318530717959
x29 = -30.3087778181038
x30 = -87.9645943005142
x31 = 9.42477796076938
x32 = -18.8495559215388
x33 = -28.2743338823081
x34 = -9.42477796076938
x35 = -39.7335557788732
x36 = 59.6902604182061
x37 = 28.2743338823081
x38 = -47.1238898038469
x39 = -3.14159265358979
x40 = 31.4159265358979
x41 = 94.2477796076938
x42 = -72.2566310325652
x43 = -84.8230016469244
x44 = 53.4070751110265
x45 = -97.3893722612836
x46 = -52.2999263932324
x47 = 37.6991118430775
x48 = -50.2654824574367
x49 = -94.2477796076938
x50 = -2.0344439357957
x51 = -40.8407044966673
x52 = -37.6991118430775
x53 = 19.9567046393328
x54 = 47.1238898038469
x55 = 91.106186954104
x56 = 41.9478532144614
x57 = 48.231038521641
x58 = -12.5663706143592
x59 = -81.6814089933346
x60 = 43.9822971502571
x61 = -78.5398163397448
x62 = -96.2822235434895
x63 = 97.3893722612836
x64 = 92.2133356718981
x65 = -31.4159265358979
x66 = 0.0
x67 = -61.7247043540018
x68 = -68.0078896611814
x69 = -21.9911485751286
x70 = 4.24874137138388
x71 = 100.530964914873
x72 = 34.5575191894877
x73 = 65.9734457253857
x74 = -62.8318530717959
x75 = -53.4070751110265
x76 = 40.8407044966673
x77 = -6.28318530717959
x78 = 25.1327412287183
x79 = 85.9301503647185
x80 = 26.2398899465124
x81 = -43.9822971502571
x82 = 63.93900178959
x83 = 84.8230016469244
x84 = 72.2566310325652
x85 = -89.9990382363099
x86 = -74.2910749683609
x87 = 87.9645943005142
x87 = 87.9645943005142
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