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cos2x=1-2sin^2x la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
                    2   
cos(2*x) = 1 - 2*sin (x)
$$\cos{\left(2 x \right)} = 1 - 2 \sin^{2}{\left(x \right)}$$
Gráfica
Suma y producto de raíces [src]
suma
  3*pi        pi   pi        3*pi       
- ---- - pi - -- + -- + pi + ---- + 2*pi
   2          2    2          2         
$$\left(\left(\left(\left(\left(- \frac{3 \pi}{2} - \pi\right) - \frac{\pi}{2}\right) + \frac{\pi}{2}\right) + \pi\right) + \frac{3 \pi}{2}\right) + 2 \pi$$
=
2*pi
$$2 \pi$$
producto
  -3*pi       -pi  pi    3*pi     
0*-----*(-pi)*----*--*pi*----*2*pi
    2          2   2      2       
$$2 \pi \frac{3 \pi}{2} \pi \frac{\pi}{2} \cdot - \frac{\pi}{2} \cdot - \pi 0 \left(- \frac{3 \pi}{2}\right)$$
=
0
$$0$$
0
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
     -3*pi
x2 = -----
       2  
$$x_{2} = - \frac{3 \pi}{2}$$
x3 = -pi
$$x_{3} = - \pi$$
     -pi 
x4 = ----
      2  
$$x_{4} = - \frac{\pi}{2}$$
     pi
x5 = --
     2 
$$x_{5} = \frac{\pi}{2}$$
x6 = pi
$$x_{6} = \pi$$
     3*pi
x7 = ----
      2  
$$x_{7} = \frac{3 \pi}{2}$$
x8 = 2*pi
$$x_{8} = 2 \pi$$
x8 = 2*pi
Respuesta numérica [src]
x1 = 60.0
x2 = 0.0
x3 = 16.0
x4 = 88.0
x5 = 62.0
x6 = 58.0
x7 = -88.0
x8 = -44.0
x9 = -80.0
x10 = -3.75
x11 = 48.0
x12 = 84.0
x13 = -24.0
x14 = -98.0
x15 = 72.0
x16 = 42.0
x17 = 22.0
x18 = 82.0
x19 = -18.0
x20 = -58.0
x21 = -70.0
x22 = 24.0
x23 = -6.0
x24 = -31.75
x25 = 18.0
x26 = 94.0
x27 = 10.0
x28 = -22.0
x29 = -26.0
x30 = 46.1666666666667
x31 = -50.0
x32 = 4.125
x33 = 28.0
x34 = 26.0
x35 = 70.0
x36 = 66.0
x37 = 40.0
x38 = -78.0
x39 = 64.0
x40 = -76.0
x41 = 54.0
x42 = 98.0
x43 = -10.0
x44 = 86.0
x45 = -34.0
x46 = -12.0
x47 = 68.1666666666667
x48 = -16.0
x49 = -60.0
x50 = -94.0
x51 = -48.0
x52 = 6.0
x53 = -66.0
x54 = -74.0
x55 = -96.0
x56 = 100.0
x57 = -40.0
x58 = -67.8333333333333
x59 = -38.0
x60 = -100.0
x61 = 74.0
x62 = 52.1666666666667
x63 = -62.0
x64 = -82.0
x65 = -56.0
x66 = -64.0
x67 = 78.0
x68 = 76.0
x69 = 38.0
x70 = -7.75
x71 = 2.0
x72 = 14.25
x73 = -28.0
x74 = -45.75
x75 = 34.0
x76 = -36.0
x77 = 90.0
x78 = -2.0
x79 = 36.0
x80 = 56.0
x81 = 12.0
x82 = -90.0
x83 = 92.0833333333333
x84 = -86.0
x85 = 80.0
x86 = 50.0
x87 = 44.0
x88 = -51.8333333333333
x89 = -72.0
x90 = -20.0
x91 = 96.0
x92 = -30.0
x93 = -42.0
x94 = 20.0
x95 = -13.75
x96 = -91.75
x97 = 30.0
x98 = 7.75
x99 = -54.0
x100 = -84.0
x100 = -84.0