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cos4xcos2x=sin3xsin5x equation

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Numerical solution:

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The solution

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cos(4*x)*cos(2*x) = sin(3*x)*sin(5*x)
$$\cos{\left(2 x \right)} \cos{\left(4 x \right)} = \sin{\left(3 x \right)} \sin{\left(5 x \right)}$$
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The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
     -pi 
x1 = ----
      2
$$x_{1} = - \frac{\pi}{2}$$ 
     -3*pi
x2 = -----
       14
$$x_{2} = - \frac{3 \pi}{14}$$ 
     -pi 
x3 = ----
      14
$$x_{3} = - \frac{\pi}{14}$$ 
     pi
x4 = --
     14
$$x_{4} = \frac{\pi}{14}$$ 
     3*pi
x5 = ----
      14
$$x_{5} = \frac{3 \pi}{14}$$ 
     pi
x6 = --
     2
$$x_{6} = \frac{\pi}{2}$$ 
     11*pi
x7 = -----
       14
$$x_{7} = \frac{11 \pi}{14}$$ 
     13*pi
x8 = -----
       14
$$x_{8} = \frac{13 \pi}{14}$$ 
           / 14____\
x9 = -I*log\-\/ -1 /
$$x_{9} = - i \log{\left(- \sqrt[14]{-1} \right)}$$ 
            /     3/14\
x10 = -I*log\-(-1)    /
$$x_{10} = - i \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)}$$ 
                                                   /   /pi\\
                 /    _____________________\       |cos|--||
                 |   /    2/pi\      2/pi\ |       |   \7 /|
x11 = -pi - I*log|  /  cos |--| + sin |--| | + atan|-------|
                 \\/       \7 /       \7 / /       |   /pi\|
                                                   |sin|--||
                                                   \   \7 //
$$x_{11} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}$$ 
               /   /pi\\                                   
               |cos|--||        /    _____________________\
               |   \7 /|        |   /    2/pi\      2/pi\ |
x12 = pi - atan|-------| - I*log|  /  cos |--| + sin |--| |
               |   /pi\|        \\/       \7 /       \7 / /
               |sin|--||                                   
               \   \7 //
$$x_{12} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \pi$$ 
            /   /pi\\                                   
            |cos|--||        /    _____________________\
            |   \7 /|        |   /    2/pi\      2/pi\ |
x13 = - atan|-------| - I*log|  /  cos |--| + sin |--| |
            |   /pi\|        \\/       \7 /       \7 / /
            |sin|--||                                   
            \   \7 //
$$x_{13} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)}$$ 
                                               /   /pi\\
             /    _____________________\       |cos|--||
             |   /    2/pi\      2/pi\ |       |   \7 /|
x14 = - I*log|  /  cos |--| + sin |--| | + atan|-------|
             \\/       \7 /       \7 / /       |   /pi\|
                                               |sin|--||
                                               \   \7 //
$$x_{14} = - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}$$ 
x14 = -i*log(sqrt(sin(pi/7)^2 + cos(pi/7)^2)) + atan(cos(pi/7)/sin(pi/7))
Numerical answer [src] 
x1 = -81.905808468591
x2 = -3.81479107935903
x3 = 89.9841895778219
x4 = 10.0979763865386
x5 = 40.1675060708981
x6 = -95.8185758715514
x7 = -61.7098556955138
x8 = 74.276226309873
x9 = 14.1371666781978
x10 = 80.1106126783847
x11 = 28.0499344070517
x12 = -67.9930410026934
x13 = 92.6769831195842
x14 = 72.0322315573088
x15 = -72.0322315573088
x16 = 18.1763574957695
x17 = -58.1194641568646
x18 = 50.0410829821803
x19 = 67.9930410026934
x20 = -41.9627018729494
x21 = -50.0410829821803
x22 = -24.0107438524363
x23 = 98.0625706870528
x24 = -2.01959527730772
x25 = -65.7490462501292
x26 = 24.0107438524363
x27 = 94.0233801324374
x28 = 84.1498032211552
x29 = -59.9146598934625
x30 = 26.2547386050004
x31 = -85.9449990232065
x32 = -19.9715532978208
x33 = 19.9715532978208
x34 = 88.1889937757706
x35 = 58.1194639815683
x36 = -77.8666179139756
x37 = 0.224399475256414
x38 = 66.1978452006421
x39 = 70.2370357552575
x40 = -87.7401948252578
x41 = 6.05878583192317
x42 = 58.1194639733282
x43 = 388.884290619365
x44 = -11.8931721885899
x45 = -94.0233801324374
x46 = 62.1586546460266
x47 = -76.0714221119243
x48 = -80.1106127288493
x49 = -47.7970882296161
x50 = -33.8843207637185
x51 = -63.9538504480779
x52 = 76.0714221119243
x53 = -32.9867228544314
x54 = -17.7275585452567
x55 = -73.8274272888222
x56 = -21.7667490998721
x57 = 35.6795165657698
x58 = 32.0891249616672
x59 = -37.9235113183339
x60 = -25.8059396544876
x61 = 96.2673748850015
x62 = 54.9778717349604
x63 = -5.60998688141034
x64 = -99.8577664891041
x65 = -7.85398156908478
x66 = -29.8451301480097
x67 = -55.875469338847
x68 = -54.5290724873086
x69 = -83.7010042706423
x70 = 100.306565439617
x71 = 4.26359002987186
x72 = 52.7338766852572
x73 = 46.0018924275648
x74 = -91.7793853798732
x75 = 2.01959527730772
x76 = -28.0499344070517
x77 = -89.9841895778219
x78 = -39.7187071203852
x79 = 54.0802735367957
x80 = -10.9955743995035
x81 = 64.4026491723469
x82 = -6.05878583192317
x83 = -51.8362787100334
x84 = 86.3937983040671
x85 = -98.0625706870528
x86 = -69.7882368047447
x87 = -46.0018924275648
x88 = -15.9323627432054
x89 = 22.215548050385
x90 = 42.4115010150339
x91 = 92.2281843303861
x92 = 44.2066966255135
x93 = 48.245887180129
x94 = -43.7578976750007
x94 = -43.7578976750007
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