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3+2sin2x=tgx+ctgx la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
3 + 2*sin(2*x) = tan(x) + cot(x)
$$2 \sin{\left(2 x \right)} + 3 = \tan{\left(x \right)} + \cot{\left(x \right)}$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     pi
x1 = --
     12
$$x_{1} = \frac{\pi}{12}$$ 
     5*pi
x2 = ----
      12
$$x_{2} = \frac{5 \pi}{12}$$ 
         /    /        ___\\       /    /        ___\\
         |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||
x3 = - re|atan|- - -------|| - I*im|atan|- - -------||
         \    \2      2   //       \    \2      2   //
$$x_{3} = - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}$$ 
         /    /        ___\\       /    /        ___\\
         |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||
x4 = - re|atan|- + -------|| - I*im|atan|- + -------||
         \    \2      2   //       \    \2      2   //
$$x_{4} = - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}$$ 
x4 = -re(atan(1/2 + sqrt(3)*i/2)) - i*im(atan(1/2 + sqrt(3)*i/2))
Suma y producto de raíces [src] 
suma
                /    /        ___\\       /    /        ___\\       /    /        ___\\       /    /        ___\\
pi   5*pi       |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||
-- + ---- + - re|atan|- - -------|| - I*im|atan|- - -------|| + - re|atan|- + -------|| - I*im|atan|- + -------||
12    12        \    \2      2   //       \    \2      2   //       \    \2      2   //       \    \2      2   //
$$\left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right) + \left(\left(\frac{\pi}{12} + \frac{5 \pi}{12}\right) + \left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right)\right)$$ 
=
       /    /        ___\\     /    /        ___\\       /    /        ___\\       /    /        ___\\
pi     |    |1   I*\/ 3 ||     |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||
-- - re|atan|- + -------|| - re|atan|- - -------|| - I*im|atan|- + -------|| - I*im|atan|- - -------||
2      \    \2      2   //     \    \2      2   //       \    \2      2   //       \    \2      2   //
$$- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + \frac{\pi}{2} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}$$ 
producto
        /    /    /        ___\\       /    /        ___\\\ /    /    /        ___\\       /    /        ___\\\
pi 5*pi |    |    |1   I*\/ 3 ||       |    |1   I*\/ 3 ||| |    |    |1   I*\/ 3 ||       |    |1   I*\/ 3 |||
--*----*|- re|atan|- - -------|| - I*im|atan|- - -------|||*|- re|atan|- + -------|| - I*im|atan|- + -------|||
12  12  \    \    \2      2   //       \    \2      2   /// \    \    \2      2   //       \    \2      2   ///
$$\frac{\pi}{12} \frac{5 \pi}{12} \left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)$$ 
=
      /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\
    2 |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 ||| |    |    |1   I*\/ 3 ||     |    |1   I*\/ 3 |||
5*pi *|I*im|atan|- + -------|| + re|atan|- + -------|||*|I*im|atan|- - -------|| + re|atan|- - -------|||
      \    \    \2      2   //     \    \2      2   /// \    \    \2      2   //     \    \2      2   ///
---------------------------------------------------------------------------------------------------------
                                                   144
$$\frac{5 \pi^{2} \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)}{144}$$ 
5*pi^2*(i*im(atan(1/2 + i*sqrt(3)/2)) + re(atan(1/2 + i*sqrt(3)/2)))*(i*im(atan(1/2 - i*sqrt(3)/2)) + re(atan(1/2 - i*sqrt(3)/2)))/144
Respuesta numérica [src] 
x1 = 1549.06697760757
x2 = 32.7249234748937
x3 = 48.4328867428426
x4 = -65.7116463375865
x5 = -12.30457122656
x6 = -6.02138591938044
x7 = -89.7971900151083
x8 = 20.1585528605345
x9 = 81.9432083811338
x10 = -2013.49909156326
x11 = 92.4151838930998
x12 = -50.0036830696375
x13 = 155.247036964896
x14 = -86.6555973615185
x15 = -71.9948316447661
x16 = -93.9859802198946
x17 = 72.5184304203644
x18 = -103.410758180664
x19 = -83.5140047079287
x20 = -43.720497762458
x21 = 88.2263936883134
x22 = -21.7293491873294
x23 = 42.1497014356631
x24 = 44.2440965380563
x25 = 4.45058959258554
x26 = -67.8060414399797
x27 = -1.83259571459405
x28 = -36.3901149040818
x29 = 22.2529479629277
x30 = 86.1319985859202
x31 = -28.012534494509
x32 = 154.199839413699
x33 = 37.9609112308767
x34 = -8.11578102177363
x35 = -74.0892267471593
x36 = -45.8148928648512
x37 = -87.7027949127151
x38 = 13.8753675533549
x39 = -52.0980781720307
x40 = -23.8237442897226
x41 = -18.5877565337396
x42 = 59.9520598060052
x43 = 64.1408500107916
x44 = 15.9697626557481
x45 = 39.0081087820733
x46 = 235.881248407034
x47 = -55.2396708256205
x48 = -46.8620904160477
x49 = 29.5833308213039
x50 = 51.5744793964324
x51 = -17.540558982543
x52 = -30.1069295969022
x53 = -96.0803753222878
x54 = 66.2352451131848
x55 = -39.5317075576716
x56 = 47.3856891916461
x57 = 70.4240353179712
x58 = 98.6983692002793
x59 = 7.59218224617533
x59 = 7.59218224617533
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