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(cos(2x)-3cos(x)-1)/(sqrt(2sin(x)-1))=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
cos(2*x) - 3*cos(x) - 1    
----------------------- = 0
      ______________       
    \/ 2*sin(x) - 1
$$\frac{\left(- 3 \cos{\left(x \right)} + \cos{\left(2 x \right)}\right) - 1}{\sqrt{2 \sin{\left(x \right)} - 1}} = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     -2*pi
x1 = -----
       3
$$x_{1} = - \frac{2 \pi}{3}$$ 
     2*pi
x2 = ----
      3
$$x_{2} = \frac{2 \pi}{3}$$ 
           /      ___\
x3 = -I*log\2 - \/ 3 /
$$x_{3} = - i \log{\left(2 - \sqrt{3} \right)}$$ 
           /      ___\
x4 = -I*log\2 + \/ 3 /
$$x_{4} = - i \log{\left(\sqrt{3} + 2 \right)}$$ 
x4 = -i*log(sqrt(3) + 2)
Suma y producto de raíces [src] 
suma
  2*pi   2*pi        /      ___\        /      ___\
- ---- + ---- - I*log\2 - \/ 3 / - I*log\2 + \/ 3 /
   3      3
$$- i \log{\left(\sqrt{3} + 2 \right)} + \left(\left(- \frac{2 \pi}{3} + \frac{2 \pi}{3}\right) - i \log{\left(2 - \sqrt{3} \right)}\right)$$ 
=
       /      ___\        /      ___\
- I*log\2 + \/ 3 / - I*log\2 - \/ 3 /
$$- i \log{\left(\sqrt{3} + 2 \right)} - i \log{\left(2 - \sqrt{3} \right)}$$ 
producto
-2*pi 2*pi /      /      ___\\ /      /      ___\\
-----*----*\-I*log\2 - \/ 3 //*\-I*log\2 + \/ 3 //
  3    3
$$- i \log{\left(\sqrt{3} + 2 \right)} - i \log{\left(2 - \sqrt{3} \right)} - \frac{2 \pi}{3} \frac{2 \pi}{3}$$ 
=
    2    /      ___\    /      ___\
4*pi *log\2 + \/ 3 /*log\2 - \/ 3 /
-----------------------------------
                 9
$$\frac{4 \pi^{2} \log{\left(2 - \sqrt{3} \right)} \log{\left(\sqrt{3} + 2 \right)}}{9}$$ 
4*pi^2*log(2 + sqrt(3))*log(2 - sqrt(3))/9
Respuesta numérica [src] 
x1 = 39.7935069454707
x2 = -8.37758040957278
x3 = -83.7758040957278
x4 = -92.1533845053006
x5 = 64.9262481741891
x6 = -71.2094334813686
x7 = -67.0206432765823
x8 = -90.0589894029074
x9 = 33.5103216382911
x10 = -35.6047167406843
x11 = -52.3598775598299
x12 = -54.4542726622231
x13 = 73.3038285837618
x14 = 71.2094334813686
x15 = -39.7935069454707
x16 = -20.943951023932
x17 = 98.4365698124802
x18 = -77.4926187885482
x19 = 10.471975511966
x20 = 58.6430628670095
x21 = 79.5870138909414
x22 = 96.342174710087
x23 = 46.0766922526503
x24 = 81.6814089933346 + 1.31695789692482*i
x25 = -10.471975511966
x26 = -46.0766922526503
x27 = -25.1327412287183 + 1.31695789692482*i
x28 = -48.1710873550435
x29 = 20.943951023932
x30 = -6.28318530717959 + 1.31695789692482*i
x31 = 2.0943951023932
x32 = 41.8879020478639
x33 = -23.0383461263252
x34 = -85.870199198121
x35 = -41.8879020478639
x36 = 67.0206432765823
x37 = 37.6991118430775 + 1.31695789692482*i
x38 = -60.7374579694027
x39 = -58.6430628670095
x40 = -79.5870138909414
x41 = 54.4542726622231
x42 = -27.2271363311115
x43 = -4.18879020478639
x44 = 29.3215314335047
x45 = 23.0383461263252
x46 = 60.7374579694027
x47 = 77.4926187885482
x48 = 85.870199198121
x49 = 90.0589894029074
x50 = 8.37758040957278
x51 = 4.18879020478639
x52 = -29.3215314335047
x53 = 48.1710873550435
x54 = 35.6047167406843
x55 = -73.3038285837618
x56 = 83.7758040957278
x57 = -2.0943951023932
x58 = 14.6607657167524
x59 = 92.1533845053006
x60 = -16.7551608191456
x61 = -98.4365698124802
x62 = -96.342174710087
x63 = -64.9262481741891
x64 = 16.7551608191456
x65 = 27.2271363311115
x66 = -33.5103216382911
x67 = -14.6607657167524
x68 = 52.3598775598299
x68 = 52.3598775598299
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