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sinx+cosx/sinx=2cotx la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
         cos(x)           
sin(x) + ------ = 2*cot(x)
         sin(x)           
$$\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} = 2 \cot{\left(x \right)}$$
Gráfica
Respuesta rápida [src]
                                    /      __________________________________________________________________________________________________________________________________________________\
                                    |     /                       ___________            ___________        ___________    ____________              ____________               ____________ |
           /       ___     \        |    /        ___     ____   /       ___      ___   /       ___        /       ___    /        ___        ___   /        ___        ____   /        ___  |
           |     \/ 2      |        |   /   3   \/ 5    \/ 10 *\/  1 - \/ 5     \/ 2 *\/  1 - \/ 5     I*\/  1 - \/ 5  *\/  -1 + \/ 5     I*\/ 2 *\/  -1 + \/ 5     I*\/ 10 *\/  -1 + \/ 5   |
x1 = - atan|---------------| - I*log|  /    - - ----- - --------------------- + -------------------- - -------------------------------- - ----------------------- + ------------------------ |
           |   ____________|        \\/     2     2               4                      4                            2                              4                         4             /
           |  /        ___ |                                                                                                                                                                  
           \\/  -1 + \/ 5  /                                                                                                                                                                  
$$x_{1} = - \operatorname{atan}{\left(\frac{\sqrt{2}}{\sqrt{-1 + \sqrt{5}}} \right)} - i \log{\left(\sqrt{- \frac{\sqrt{5}}{2} - \frac{i \sqrt{-1 + \sqrt{5}} \sqrt{1 - \sqrt{5}}}{2} + \frac{3}{2} - \frac{\sqrt{10} \sqrt{1 - \sqrt{5}}}{4} - \frac{\sqrt{2} i \sqrt{-1 + \sqrt{5}}}{4} + \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{4} + \frac{\sqrt{10} i \sqrt{-1 + \sqrt{5}}}{4}} \right)}$$
            /      __________________________________________________________________________________________________________________________________________________\                        
            |     /                      ___________             ___________        ___________    ____________               ____________              ____________ |                        
            |    /        ___     ___   /       ___      ____   /       ___        /       ___    /        ___        ____   /        ___        ___   /        ___  |       /       ___     \
            |   /   3   \/ 5    \/ 2 *\/  1 - \/ 5     \/ 10 *\/  1 - \/ 5     I*\/  1 - \/ 5  *\/  -1 + \/ 5     I*\/ 10 *\/  -1 + \/ 5     I*\/ 2 *\/  -1 + \/ 5   |       |     \/ 2      |
x2 = - I*log|  /    - - ----- - -------------------- + --------------------- - -------------------------------- - ------------------------ + ----------------------- | + atan|---------------|
            \\/     2     2              4                       4                            2                              4                          4            /       |   ____________|
                                                                                                                                                                             |  /        ___ |
                                                                                                                                                                             \\/  -1 + \/ 5  /
$$x_{2} = - i \log{\left(\sqrt{- \frac{\sqrt{5}}{2} - \frac{i \sqrt{-1 + \sqrt{5}} \sqrt{1 - \sqrt{5}}}{2} + \frac{3}{2} - \frac{\sqrt{10} i \sqrt{-1 + \sqrt{5}}}{4} - \frac{\sqrt{2} \sqrt{1 - \sqrt{5}}}{4} + \frac{\sqrt{2} i \sqrt{-1 + \sqrt{5}}}{4} + \frac{\sqrt{10} \sqrt{1 - \sqrt{5}}}{4}} \right)} + \operatorname{atan}{\left(\frac{\sqrt{2}}{\sqrt{-1 + \sqrt{5}}} \right)}$$
               /               2                \
x3 = pi + I*log|--------------------------------|
               |                     ___________|
               |      ___     ___   /       ___ |
               \1 + \/ 5  + \/ 2 *\/  1 + \/ 5  /
$$x_{3} = \pi + i \log{\left(\frac{2}{1 + \sqrt{5} + \sqrt{2} \sqrt{1 + \sqrt{5}}} \right)}$$
               /               2                \
x4 = pi + I*log|--------------------------------|
               |                     ___________|
               |      ___     ___   /       ___ |
               \1 + \/ 5  - \/ 2 *\/  1 + \/ 5  /
$$x_{4} = \pi + i \log{\left(\frac{2}{- \sqrt{2} \sqrt{1 + \sqrt{5}} + 1 + \sqrt{5}} \right)}$$
x4 = pi + i*log(2/(-sqrt(2)*sqrt(1 + sqrt(5)) + 1 + sqrt(5)))
Respuesta numérica [src]
x1 = -43.0777402559547
x2 = -44.8868540445595
x3 = -49.3609255631343
x4 = 7.18774220148197
x5 = 87.0600374062118
x6 = -82.585965887637
x7 = -93.3432227133914
x8 = 88.8691511948166
x9 = -38.6036687373799
x10 = -87.0600374062118
x11 = -7.18774220148197
x12 = 43.0777402559547
x13 = 80.7768520990322
x14 = -88.8691511948166
x15 = 32.3204834302003
x16 = -95.1523365019962
x17 = 11.6618137200568
x18 = 82.585965887637
x19 = -13.4709275086616
x20 = 95.1523365019962
x21 = -55.6441108703139
x22 = 70.0195952732778
x23 = -17.9449990272364
x24 = -24.228184334416
x25 = 55.6441108703139
x26 = -0.904556894302381
x27 = -80.7768520990322
x28 = -51.1700393517391
x29 = 99.626408020571
x30 = 51.1700393517391
x31 = 57.4532246589187
x32 = -61.9272961774935
x33 = -26.0372981230207
x34 = 93.3432227133914
x35 = -63.7364099660982
x36 = 19.7541128158411
x37 = 74.4936667918527
x38 = -30.5113696415956
x39 = 36.7945549487751
x40 = 17.9449990272364
x41 = -5.37862841287721
x42 = 26.0372981230207
x43 = -68.2104814846731
x44 = -76.3027805804574
x45 = 44.8868540445595
x46 = -36.7945549487751
x47 = 24.228184334416
x48 = -19.7541128158411
x49 = 13.4709275086616
x50 = -32.3204834302003
x51 = 0.904556894302381
x52 = -70.0195952732778
x53 = -11.6618137200568
x54 = -57.4532246589187
x55 = 63.7364099660982
x56 = 5.37862841287721
x57 = 68.2104814846731
x58 = 49.3609255631343
x59 = 30.5113696415956
x60 = 61.9272961774935
x61 = 76.3027805804574
x62 = -99.626408020571
x63 = -74.4936667918527
x64 = 38.6036687373799
x64 = 38.6036687373799