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sinx^2+1/2sin2x-2cosx^2=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   2      sin(2*x)        2       
sin (x) + -------- - 2*cos (x) = 0
             2
$$\left(\sin^{2}{\left(x \right)} + \frac{\sin{\left(2 x \right)}}{2}\right) - 2 \cos^{2}{\left(x \right)} = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
pi                    /log(5)      /  ___\\                /log(5)      /  ___\\        /   ___\
-- + pi - atan(2) + I*|------ - log\\/ 5 /| + -atan(2) + I*|------ - log\\/ 5 /| - I*log\-\/ I /
4                     \  2                /                \  2                /
$$- i \log{\left(- \sqrt{i} \right)} + \left(\left(\frac{\pi}{4} + \left(- \operatorname{atan}{\left(2 \right)} + \pi + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right) + \left(- \operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right)$$ 
=
             5*pi        /   ___\       /log(5)      /  ___\\
-2*atan(2) + ---- - I*log\-\/ I / + 2*I*|------ - log\\/ 5 /|
              4                         \  2                /
$$- i \log{\left(- \sqrt{i} \right)} - 2 \operatorname{atan}{\left(2 \right)} + \frac{5 \pi}{4} + 2 i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$ 
producto
pi /                 /log(5)      /  ___\\\ /             /log(5)      /  ___\\\ /      /   ___\\
--*|pi - atan(2) + I*|------ - log\\/ 5 /||*|-atan(2) + I*|------ - log\\/ 5 /||*\-I*log\-\/ I //
4  \                 \  2                // \             \  2                //
$$- i \log{\left(- \sqrt{i} \right)} \frac{\pi}{4} \left(- \operatorname{atan}{\left(2 \right)} + \pi + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) \left(- \operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)$$ 
=
                               /   ___\
pi*I*(pi - atan(2))*atan(2)*log\-\/ I /
---------------------------------------
                   4
$$\frac{i \pi \left(\pi - \operatorname{atan}{\left(2 \right)}\right) \log{\left(- \sqrt{i} \right)} \operatorname{atan}{\left(2 \right)}}{4}$$ 
pi*i*(pi - atan(2))*atan(2)*log(-sqrt(i))/4
Respuesta rápida [src] 
     pi
x1 = --
     4
$$x_{1} = \frac{\pi}{4}$$ 
                      /log(5)      /  ___\\
x2 = pi - atan(2) + I*|------ - log\\/ 5 /|
                      \  2                /
$$x_{2} = - \operatorname{atan}{\left(2 \right)} + \pi + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$ 
                  /log(5)      /  ___\\
x3 = -atan(2) + I*|------ - log\\/ 5 /|
                  \  2                /
$$x_{3} = - \operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$ 
           /   ___\
x4 = -I*log\-\/ I /
$$x_{4} = - i \log{\left(- \sqrt{i} \right)}$$ 
x4 = -i*log(-sqrt(i))
Respuesta numérica [src] 
x1 = 39.7335557788732
x2 = -46.3384916404494
x3 = 30.3087778181038
x4 = 38.484510006475
x5 = -54.5142238288206
x6 = -87.1791961371168
x7 = 83.7158529291303
x8 = -2.35619449019234
x9 = 32.2013246992954
x10 = 60.4756585816035
x11 = -73.3637797503593
x12 = 77.4326676219507
x13 = 8.31762924297529
x14 = 89.9990382363099
x15 = -41.9478532144614
x16 = -26.2398899465124
x17 = 17.7424072037447
x18 = 2190.47547771548
x19 = 47.9092879672443
x20 = -13.6735193321533
x21 = -32.523075253692
x22 = 2.0344439357957
x23 = 11.4592218965651
x24 = 54.1924732744239
x25 = -51.3726311752308
x26 = 19.6349540849362
x27 = 69.9004365423729
x28 = -65.1880475619882
x29 = -4.24874137138388
x30 = 14.6008145501549
x31 = 68.0078896611814
x32 = -21.2057504117311
x33 = -48.231038521641
x34 = -24.3473430653209
x35 = 74.2910749683609
x36 = 16.4933614313464
x37 = 25.9181393921158
x38 = -33.7721210260903
x39 = -70.2221870967695
x40 = 46.0167410860528
x41 = 58.583111700412
x42 = 80.5742602755405
x43 = -7.39033402497368
x44 = 44.7676953136546
x45 = 33.4503704716936
x46 = 55.4415190468222
x47 = -85.9301503647185
x48 = 22.776546738526
x49 = -62.0464549083984
x50 = -49.4800842940392
x51 = -5.49778714378214
x52 = -10.5319266785635
x53 = 10.2101761241668
x54 = 61.7247043540018
x55 = 76.1836218495525
x56 = -55.7632696012188
x57 = -93.4623814442964
x58 = -40.0553063332699
x59 = 0.785398163397448
x60 = -35.6646679072818
x61 = -68.329640215578
x62 = -29.3814826001022
x63 = 91.8915851175014
x64 = -99.7455667514759
x65 = 66.7588438887831
x66 = -98.4965209790777
x67 = -90.3207887907066
x68 = 96.2822235434895
x69 = -77.7544181763474
x70 = -63.93900178959
x71 = 3.92699081698724
x72 = -18.0641577581413
x73 = -84.037603483527
x74 = 24.0255925109243
x75 = -11.7809724509617
x76 = 88.7499924639117
x77 = 99.4238161970793
x78 = 52.2999263932324
x79 = -43.1968989868597
x80 = 36.5919631252834
x81 = -71.4712328691678
x82 = -27.4889357189107
x83 = 82.4668071567321
x84 = -95.3549283254879
x85 = 102.565408850669
x86 = 63.6172512351933
x87 = -57.6558164824104
x88 = -92.2133356718981
x89 = 85.6083998103219
x90 = 41.6261026600648
x91 = 98.174770424681
x92 = 137.122928040157
x93 = -19.9567046393328
x94 = -76.5053724039491
x95 = -79.6469650575389
x95 = -79.6469650575389
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