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sqrt(cos(2*x)-5*sin(x))=-2*cos(x) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
  _____________________            
\/ cos(2*x) - 5*sin(x)  = -2*cos(x)
$$\sqrt{- 5 \sin{\left(x \right)} + \cos{\left(2 x \right)}} = - 2 \cos{\left(x \right)}$$
Gráfica
Respuesta rápida [src]
     -5*pi
x1 = -----
       6  
$$x_{1} = - \frac{5 \pi}{6}$$
     pi        /        ___\
x2 = -- - I*log\3 - 2*\/ 2 /
     2                      
$$x_{2} = \frac{\pi}{2} - i \log{\left(3 - 2 \sqrt{2} \right)}$$
x2 = pi/2 - i*log(3 - 2*sqrt(2))
Suma y producto de raíces [src]
suma
  5*pi   pi        /        ___\
- ---- + -- - I*log\3 - 2*\/ 2 /
   6     2                      
$$- \frac{5 \pi}{6} + \left(\frac{\pi}{2} - i \log{\left(3 - 2 \sqrt{2} \right)}\right)$$
=
  pi        /        ___\
- -- - I*log\3 - 2*\/ 2 /
  3                      
$$- \frac{\pi}{3} - i \log{\left(3 - 2 \sqrt{2} \right)}$$
producto
-5*pi /pi        /        ___\\
-----*|-- - I*log\3 - 2*\/ 2 /|
  6   \2                      /
$$- \frac{5 \pi}{6} \left(\frac{\pi}{2} - i \log{\left(3 - 2 \sqrt{2} \right)}\right)$$
=
     /             /        ___\\
5*pi*\-pi + 2*I*log\3 - 2*\/ 2 //
---------------------------------
                12               
$$\frac{5 \pi \left(- \pi + 2 i \log{\left(3 - 2 \sqrt{2} \right)}\right)}{12}$$
5*pi*(-pi + 2*i*log(3 - 2*sqrt(2)))/12
Respuesta numérica [src]
x1 = -15.1843644923507
x2 = -40.317105721069
x3 = -96.8657734856853
x4 = -2.61799387799149
x5 = 35.081117965086
x6 = 41.3643032722656
x7 = -65.4498469497874
x8 = -52.8834763354282
x9 = 97.9129710368819
x10 = -34.0339204138894
x11 = 16.2315620435473
x12 = -21.4675497995303
x13 = -78.0162175641465
x14 = 85.3466004225227
x15 = -90.5825881785057
x16 = 72.7802298081635
x17 = 9.94837673636768
x18 = -59.1666616426078
x19 = 60.2138591938044
x20 = 91.6297857297023
x21 = 79.0634151153431
x22 = 66.497044500984
x23 = -27.7507351067098
x24 = -71.733032256967
x25 = -46.6002910282486
x26 = 22.5147473507269
x27 = 53.9306738866248
x28 = -8.90117918517108
x29 = 47.6474885794452
x30 = -84.2994028713261
x31 = 3.66519142918809
x32 = 28.7979326579064
x32 = 28.7979326579064