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(1+cos(2*x)-sin(2*x))/cos(x)-sin(x)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
1 + cos(2*x) - sin(2*x)             
----------------------- - sin(x) = 0
         cos(x)                     
$$\frac{\left(\cos{\left(2 x \right)} + 1\right) - \sin{\left(2 x \right)}}{\cos{\left(x \right)}} - \sin{\left(x \right)} = 0$$
Gráfica
Respuesta rápida [src]
             /log(13)      /  ____\\            
x1 = -pi + I*|------- - log\\/ 13 /| + atan(2/3)
             \   2                 /            
$$x_{1} = - \pi + \operatorname{atan}{\left(\frac{2}{3} \right)} + i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)$$
       /log(13)      /  ____\\            
x2 = I*|------- - log\\/ 13 /| + atan(2/3)
       \   2                 /            
$$x_{2} = \operatorname{atan}{\left(\frac{2}{3} \right)} + i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)$$
x2 = atan(2/3) + i*(-log(sqrt(13)) + log(13)/2)
Suma y producto de raíces [src]
suma
        /log(13)      /  ____\\                 /log(13)      /  ____\\            
-pi + I*|------- - log\\/ 13 /| + atan(2/3) + I*|------- - log\\/ 13 /| + atan(2/3)
        \   2                 /                 \   2                 /            
$$\left(- \pi + \operatorname{atan}{\left(\frac{2}{3} \right)} + i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)\right) + \left(\operatorname{atan}{\left(\frac{2}{3} \right)} + i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)\right)$$
=
                        /log(13)      /  ____\\
-pi + 2*atan(2/3) + 2*I*|------- - log\\/ 13 /|
                        \   2                 /
$$- \pi + 2 \operatorname{atan}{\left(\frac{2}{3} \right)} + 2 i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)$$
producto
/        /log(13)      /  ____\\            \ /  /log(13)      /  ____\\            \
|-pi + I*|------- - log\\/ 13 /| + atan(2/3)|*|I*|------- - log\\/ 13 /| + atan(2/3)|
\        \   2                 /            / \  \   2                 /            /
$$\left(\operatorname{atan}{\left(\frac{2}{3} \right)} + i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)\right) \left(- \pi + \operatorname{atan}{\left(\frac{2}{3} \right)} + i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)\right)$$
=
(-pi + atan(2/3))*atan(2/3)
$$\left(- \pi + \operatorname{atan}{\left(\frac{2}{3} \right)}\right) \operatorname{atan}{\left(\frac{2}{3} \right)}$$
(-pi + atan(2/3))*atan(2/3)
Respuesta numérica [src]
x1 = 0.588002603547568
x2 = -65.3854431218381
x3 = 57.1366703681638
x4 = 35.1455217930353
x5 = 53.9950777145741
x6 = -46.5358872002993
x7 = 44.5702997538047
x8 = -18.2615533179912
x9 = 242.490636929962
x10 = 10.0127805643169
x11 = 19.4375585250863
x12 = 91.6941895576516
x13 = 82.2694115968822
x14 = -99.9429623113258
x15 = 79.1278189432924
x16 = 16.2959658714965
x17 = 69.703040982523
x18 = -87.3765916969666
x19 = -90.5181843505564
x20 = 25.7207438322659
x21 = 47.7118924073945
x22 = 6.87118791072715
x23 = 94.8357822112414
x24 = 85.411004250472
x25 = -11.9783680108116
x26 = -43.3942945467095
x27 = 97.9773748648312
x28 = -84.2349990433768
x29 = -5.69518270363202
x30 = -59.1022578146585
x31 = -27.6863312787606
x32 = 88.5525969040618
x33 = -96.801369657736
x34 = -52.8190725074789
x35 = -37.11110923953
x36 = -24.5447386251708
x37 = -71.6686284290177
x38 = 50.8534850609843
x39 = -33.9695165859402
x40 = 75.9862262897026
x41 = -62.2438504682483
x42 = -49.6774798538891
x43 = -40.2527018931197
x44 = -55.9606651610687
x45 = -21.403145971581
x46 = 60.2782630217536
x47 = 38.2871144466251
x48 = -2.55359005004223
x49 = 66.5614483289332
x50 = 32.0039291394455
x51 = 41.4287071002149
x52 = 22.5791511786761
x53 = -15.1199606644014
x54 = -77.9518137361973
x55 = -106.226147618505
x56 = 3.72959525713736
x57 = -74.8102210826075
x58 = 28.8623364858557
x59 = 101.118967518421
x60 = -8.83677535722181
x61 = 72.8446336361128
x62 = 182.800376511756
x63 = -30.8279239323504
x64 = 63.4198556753434
x65 = 13.1543732179067
x66 = -93.6597770041462
x67 = -68.5270357754279
x68 = -81.0934063897871
x68 = -81.0934063897871