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(cos(2*x)*cos(8*x)-cos(10*x))/cos(x+1)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
cos(2*x)*cos(8*x) - cos(10*x)    
----------------------------- = 0
          cos(x + 1)
cos⁡(2x)cos⁡(8x)−cos⁡(10x)cos⁡(x+1)=0\frac{\cos{\left(2 x \right)} \cos{\left(8 x \right)} - \cos{\left(10 x \right)}}{\cos{\left(x + 1 \right)}} = 0
Simplificar
Gráfica
0-80-60-40-2020406080-100100-50005000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 0
x1=0x_{1} = 0 
     -7*pi
x2 = -----
       8
x2=−7π8x_{2} = - \frac{7 \pi}{8} 
     -3*pi
x3 = -----
       4
x3=−3π4x_{3} = - \frac{3 \pi}{4} 
     -pi 
x4 = ----
      2
x4=−π2x_{4} = - \frac{\pi}{2} 
     -3*pi
x5 = -----
       8
x5=−3π8x_{5} = - \frac{3 \pi}{8} 
     -pi 
x6 = ----
      4
x6=−π4x_{6} = - \frac{\pi}{4} 
     pi
x7 = --
     8
x7=π8x_{7} = \frac{\pi}{8} 
     pi
x8 = --
     4
x8=π4x_{8} = \frac{\pi}{4} 
     pi
x9 = --
     2
x9=π2x_{9} = \frac{\pi}{2} 
      5*pi
x10 = ----
       8
x10=5π8x_{10} = \frac{5 \pi}{8} 
      3*pi
x11 = ----
       4
x11=3π4x_{11} = \frac{3 \pi}{4} 
x12 = pi
x12=πx_{12} = \pi 
                                      /   ___________      ___________\
                                      |  /       ___      /       ___ |
        /log(8)      /    ___\\       |\/  2 + \/ 2   + \/  2 - \/ 2  |
x13 = I*|------ - log\2*\/ 2 /| + atan|-------------------------------|
        \  2                  /       |   ___________      ___________|
                                      |  /       ___      /       ___ |
                                      \\/  2 + \/ 2   - \/  2 - \/ 2  /
x13=atan⁡(2−2+2+2−2−2+2+2)+i(−log⁡(22)+log⁡(8)2)x_{13} = \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right) 
                                      /   ___________      ___________\
                                      |  /       ___      /       ___ |
        /log(8)      /    ___\\       |\/  2 - \/ 2   - \/  2 + \/ 2  |
x14 = I*|------ - log\2*\/ 2 /| + atan|-------------------------------|
        \  2                  /       |   ___________      ___________|
                                      |  /       ___      /       ___ |
                                      \\/  2 + \/ 2   + \/  2 - \/ 2  /
x14=atan⁡(−2+2+2−22−2+2+2)+i(−log⁡(22)+log⁡(8)2)x_{14} = \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right) 
                                           /    ___________      ___________ \
                                           |   /       ___      /       ___  |
             /log(8)      /    ___\\       | \/  2 + \/ 2   - \/  2 - \/ 2   |
x15 = pi + I*|------ - log\2*\/ 2 /| + atan|---------------------------------|
             \  2                  /       |     ___________      ___________|
                                           |    /       ___      /       ___ |
                                           \- \/  2 + \/ 2   - \/  2 - \/ 2  /
x15=atan⁡(−2−2+2+2−2+2−2−2)+π+i(−log⁡(22)+log⁡(8)2)x_{15} = \operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right) 
                / /     ___________      ___________\ \                            
                | |    /       ___      /       ___ | |                            
                |-\- \/  2 + \/ 2   - \/  2 - \/ 2  / |     /log(8)      /    ___\\
x16 = -pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /|
                |      ___________      ___________   |     \  2                  /
                |     /       ___      /       ___    |                            
                \   \/  2 - \/ 2   - \/  2 + \/ 2     /
x16=−π−atan⁡(−−2+2−2−2−2+2+2−2)+i(−log⁡(22)+log⁡(8)2)x_{16} = - \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right) 
x16 = -pi - atan(-(-sqrt(sqrt(2) + 2) - sqrt(2 - sqrt(2)))/(-sqrt(sqrt(2) + 2) + sqrt(2 - sqrt(2)))) + i*(-log(2*sqrt(2)) + log(8)/2)
Suma y producto de raíces [src] 
suma
                                                                                                   /   ___________      ___________\                                   /   ___________      ___________\                                        /    ___________      ___________ \             / /     ___________      ___________\ \                            
                                                                                                   |  /       ___      /       ___ |                                   |  /       ___      /       ___ |                                        |   /       ___      /       ___  |             | |    /       ___      /       ___ | |                            
  7*pi   3*pi   pi   3*pi   pi   pi   pi   pi   5*pi   3*pi          /log(8)      /    ___\\       |\/  2 + \/ 2   + \/  2 - \/ 2  |     /log(8)      /    ___\\       |\/  2 - \/ 2   - \/  2 + \/ 2  |          /log(8)      /    ___\\       | \/  2 + \/ 2   - \/  2 - \/ 2   |             |-\- \/  2 + \/ 2   - \/  2 - \/ 2  / |     /log(8)      /    ___\\
- ---- - ---- - -- - ---- - -- + -- + -- + -- + ---- + ---- + pi + I*|------ - log\2*\/ 2 /| + atan|-------------------------------| + I*|------ - log\2*\/ 2 /| + atan|-------------------------------| + pi + I*|------ - log\2*\/ 2 /| + atan|---------------------------------| + -pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /|
   8      4     2     8     4    8    4    2     8      4            \  2                  /       |   ___________      ___________|     \  2                  /       |   ___________      ___________|          \  2                  /       |     ___________      ___________|             |      ___________      ___________   |     \  2                  /
                                                                                                   |  /       ___      /       ___ |                                   |  /       ___      /       ___ |                                        |    /       ___      /       ___ |             |     /       ___      /       ___    |                            
                                                                                                   \\/  2 + \/ 2   - \/  2 - \/ 2  /                                   \\/  2 + \/ 2   + \/  2 - \/ 2  /                                        \- \/  2 + \/ 2   - \/  2 - \/ 2  /             \   \/  2 - \/ 2   - \/  2 + \/ 2     /
(((((((((((((−7π8−3π4)−π2)−3π8)−π4)+π8)+π4)+π2)+5π8)+3π4)+π)+(atan⁡(2−2+2+2−2−2+2+2)+i(−log⁡(22)+log⁡(8)2)))+(atan⁡(−2+2+2−22−2+2+2)+i(−log⁡(22)+log⁡(8)2)))+(atan⁡(−2−2+2+2−2+2−2−2)+π+i(−log⁡(22)+log⁡(8)2)))+(−π−atan⁡(−−2+2−2−2−2+2+2−2)+i(−log⁡(22)+log⁡(8)2))\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(- \frac{7 \pi}{8} - \frac{3 \pi}{4}\right) - \frac{\pi}{2}\right) - \frac{3 \pi}{8}\right) - \frac{\pi}{4}\right) + \frac{\pi}{8}\right) + \frac{\pi}{4}\right) + \frac{\pi}{2}\right) + \frac{5 \pi}{8}\right) + \frac{3 \pi}{4}\right) + \pi\right) + \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(- \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) 
=
         / /     ___________      ___________\ \                                     /   ___________      ___________\       /   ___________      ___________\       /    ___________      ___________ \
         | |    /       ___      /       ___ | |                                     |  /       ___      /       ___ |       |  /       ___      /       ___ |       |   /       ___      /       ___  |
pi       |-\- \/  2 + \/ 2   - \/  2 - \/ 2  / |       /log(8)      /    ___\\       |\/  2 - \/ 2   - \/  2 + \/ 2  |       |\/  2 + \/ 2   + \/  2 - \/ 2  |       | \/  2 + \/ 2   - \/  2 - \/ 2   |
-- - atan|-------------------------------------| + 4*I*|------ - log\2*\/ 2 /| + atan|-------------------------------| + atan|-------------------------------| + atan|---------------------------------|
2        |      ___________      ___________   |       \  2                  /       |   ___________      ___________|       |   ___________      ___________|       |     ___________      ___________|
         |     /       ___      /       ___    |                                     |  /       ___      /       ___ |       |  /       ___      /       ___ |       |    /       ___      /       ___ |
         \   \/  2 - \/ 2   - \/  2 + \/ 2     /                                     \\/  2 + \/ 2   + \/  2 - \/ 2  /       \\/  2 + \/ 2   - \/  2 - \/ 2  /       \- \/  2 + \/ 2   - \/  2 - \/ 2  /
atan⁡(−2+2+2−22−2+2+2)+atan⁡(−2−2+2+2−2+2−2−2)−atan⁡(−−2+2−2−2−2+2+2−2)+atan⁡(2−2+2+2−2−2+2+2)+π2+4i(−log⁡(22)+log⁡(8)2)\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + \operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + \frac{\pi}{2} + 4 i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right) 
producto
                                                    /                                /   ___________      ___________\\ /                                /   ___________      ___________\\ /                                     /    ___________      ___________ \\ /          / /     ___________      ___________\ \                            \
                                                    |                                |  /       ___      /       ___ || |                                |  /       ___      /       ___ || |                                     |   /       ___      /       ___  || |          | |    /       ___      /       ___ | |                            |
  -7*pi -3*pi -pi  -3*pi -pi  pi pi pi 5*pi 3*pi    |  /log(8)      /    ___\\       |\/  2 + \/ 2   + \/  2 - \/ 2  || |  /log(8)      /    ___\\       |\/  2 - \/ 2   - \/  2 + \/ 2  || |       /log(8)      /    ___\\       | \/  2 + \/ 2   - \/  2 - \/ 2   || |          |-\- \/  2 + \/ 2   - \/  2 - \/ 2  / |     /log(8)      /    ___\\|
0*-----*-----*----*-----*----*--*--*--*----*----*pi*|I*|------ - log\2*\/ 2 /| + atan|-------------------------------||*|I*|------ - log\2*\/ 2 /| + atan|-------------------------------||*|pi + I*|------ - log\2*\/ 2 /| + atan|---------------------------------||*|-pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /||
    8     4    2     8    4   8  4  2   8    4      |  \  2                  /       |   ___________      ___________|| |  \  2                  /       |   ___________      ___________|| |       \  2                  /       |     ___________      ___________|| |          |      ___________      ___________   |     \  2                  /|
                                                    |                                |  /       ___      /       ___ || |                                |  /       ___      /       ___ || |                                     |    /       ___      /       ___ || |          |     /       ___      /       ___    |                            |
                                                    \                                \\/  2 + \/ 2   - \/  2 - \/ 2  // \                                \\/  2 + \/ 2   + \/  2 - \/ 2  // \                                     \- \/  2 + \/ 2   - \/  2 - \/ 2  // \          \   \/  2 - \/ 2   - \/  2 + \/ 2     /                            /
π3π45π8π2π4π8⋅−π4⋅−3π8⋅−π2⋅−3π4⋅0(−7π8)(atan⁡(2−2+2+2−2−2+2+2)+i(−log⁡(22)+log⁡(8)2))(atan⁡(−2+2+2−22−2+2+2)+i(−log⁡(22)+log⁡(8)2))(atan⁡(−2−2+2+2−2+2−2−2)+π+i(−log⁡(22)+log⁡(8)2))(−π−atan⁡(−−2+2−2−2−2+2+2−2)+i(−log⁡(22)+log⁡(8)2))\pi \frac{3 \pi}{4} \frac{5 \pi}{8} \frac{\pi}{2} \frac{\pi}{4} \frac{\pi}{8} \cdot - \frac{\pi}{4} \cdot - \frac{3 \pi}{8} \cdot - \frac{\pi}{2} \cdot - \frac{3 \pi}{4} \cdot 0 \left(- \frac{7 \pi}{8}\right) \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(- \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) 
=
0
00 
0
Respuesta numérica [src] 
x1 = 18.0641577581413
x2 = -42.0188017417635
x3 = 48.3019870489431
x4 = 67.5442420454388
x5 = 8.24668071567321
x6 = 26.3108384738145
x7 = -1.17809724509617
x8 = -69.9004365423729
x9 = 32.2013246992954
x10 = -59.6902604145283
x11 = 16.8860605130451
x12 = 6.28318529141633
x13 = -73.4347282776614
x14 = 20.4203524731077
x15 = -9.8174770424681
x16 = -91.8915851175014
x17 = -29.8451301715428
x18 = 23.9546439836222
x19 = -21.9911485864382
x20 = 40.4480054149686
x21 = 78.1471172580461
x22 = -64.009950316892
x23 = -51.8362787249935
x24 = -37.6991118538739
x25 = 0.0
x26 = 30.2378292908018
x27 = 54.1924732744239
x28 = 38.0918109247762
x29 = 80.1106126339156
x30 = -81.6814089045123
x31 = 28.2743338686982
x32 = 45.9457925587507
x33 = 74.2201264410589
x34 = -39.2699081523845
x35 = -13.7444678594553
x36 = -47.9092879672443
x37 = 21.991148585099
x38 = -15.7079632834017
x39 = 40.0553063332699
x40 = 87.9645943322485
x41 = -33.7721210260903
x42 = 56.1559686829176
x43 = 65.9734457512637
x44 = -35.7356164345839
x45 = 60.0829594999048
x46 = 100.138265833175
x47 = 86.0010988920206
x48 = -25.9181393921158
x49 = -43.9822971742253
x50 = -14.1371669179543
x51 = 52.2289778659303
x52 = -91.1061869460365
x53 = -81.6814089434166
x54 = 10.2101761241668
x55 = 76.1836218495525
x56 = 90.3207887907066
x57 = -53.7997741927252
x58 = -95.8185758784677
x59 = -59.2975613365073
x60 = -3.92699081698724
x61 = 43.9822971688611
x62 = -55.7632696012188
x63 = -93.4623814442964
x64 = -75.7909227678538
x65 = -99.7455667514759
x66 = -65.9734457633372
x67 = -73.8274272990483
x68 = -31.8086256175967
x69 = 70.2931356240716
x70 = 12.1736715326604
x71 = -70.6858345144626
x72 = -77.7544181763474
x73 = 36.5210145979813
x74 = 4.31968989868597
x75 = 1.96349540849362
x76 = -11.7809724509617
x77 = -60.8683576633022
x78 = -97.7820713429823
x79 = 34.164820107789
x80 = 96.2112750161874
x81 = 72.2566310279465
x82 = -31.4159265611996
x83 = 82.0741080750334
x84 = 62.0464549083984
x85 = -86.0010988920206
x86 = -20.0276531666349
x87 = 59.6902604252636
x88 = 92.2842841992002
x89 = 98.174770424681
x90 = -87.9645943536112
x91 = 50.2654824476622
x92 = 94.2477796093768
x93 = 84.037603483527
x93 = 84.037603483527
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