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Sin(5x)+cos(5x)=sqrt(2)cos(x) equation

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Numerical solution:

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The solution

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sin(5*x) + cos(5*x) = \/ 2 *cos(x)
$$\sin{\left(5 x \right)} + \cos{\left(5 x \right)} = \sqrt{2} \cos{\left(x \right)}$$
The graph
Sum and product of roots [src]
sum
0
$$0$$
=
0
$$0$$
product
1
$$1$$
=
1
$$1$$
1
Numerical answer [src]
x1 = -52.2289778659303
x2 = 22.1874981159779
x3 = 83.9067037896274
x4 = 4.31968989868597
x5 = -15.5770635740494
x6 = 2.22529479629277
x7 = -35.9319659754333
x8 = 36.324665057132
x9 = 26.3108384738145
x10 = 81.877758534184
x11 = -6.08683576633022
x12 = 39.9244066393703
x13 = -50.0691329165873
x14 = 0.196349540849362
x15 = 46.2075919465499
x16 = 44.1786466911065
x17 = -23.9546439836222
x18 = 96.0149254753381
x19 = -100.400065220974
x20 = -72.0602814917159
x21 = -70.0313362362725
x22 = -94.0514300668444
x23 = 42.0188017417635
x24 = -59.5593607243065
x25 = -99.3528676697772
x26 = -29.6487806682537
x27 = -41.7570023539643
x28 = -1.96349540849362
x29 = 17.4751091355932
x30 = 64.009950316892
x31 = 17.9332580642417
x32 = 50.3963821513363
x33 = -95.6222263936393
x34 = 79.717913584841
x35 = -28.0779843414588
x36 = 52.4907772537295
x37 = 8.05033117482385
x38 = -21.7947990342792
x39 = -45.9457925587507
x40 = 73.4347282776614
x41 = 15.9043128087983
x42 = -79.9142631256904
x43 = 10.6028752058656
x44 = -7.65763209312512
x45 = 59.8866099590554
x46 = -43.7859476094077
x47 = -81.550509299435
x48 = 37.8954613839269
x49 = -17.6714586764426
x50 = -85.7392995042214
x51 = -48.0401876611439
x52 = -89.9280897090078
x53 = -63.7481509290929
x54 = 48.3019870489431
x55 = 94.3786793015934
x56 = 56.7450173054656
x57 = -57.9231145505618
x58 = 80.3069622073891
x59 = -65.7770961845363
x60 = 58.3158136322605
x61 = -34.3611696486384
x62 = 70.2931356240716
x63 = 68.1987405216784
x64 = -87.7682447596649
x65 = -92.022484811401
x66 = 86.0010988920206
x67 = -51.6399292433822
x68 = 61.9155552144988
x69 = 92.2842841992002
x70 = 66.169795266235
x71 = -78.4089166458453
x72 = 14.3335164820034
x73 = -4.05789051088682
x74 = 72.3875307264648
x75 = -73.6310778185108
x76 = -67.9369411338793
x77 = 101.70906215997
x78 = -75.2673239922555
x79 = 20.0276531666349
x80 = 24.2164433714213
x81 = 74.0237769002095
x82 = -83.6449044018282
x83 = -19.7658537788358
x84 = -61.6537558266997
x85 = -26.0490390860154
x86 = 59.8211601121056
x87 = -39.6626072515711
x88 = -13.9408174003047
x89 = -37.5682121491779
x90 = 30.0414797499524
x91 = 52.0326283250809
x92 = 6.41408500107916
x93 = -57.4649656219133
x94 = 28.4052335762077
x95 = 90.189889096807
x95 = 90.189889096807