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(tanx+2)(cosx-1)=0 equation

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Numerical solution:

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The solution

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(tan(x) + 2)*(cos(x) - 1) = 0
$$\left(\cos{\left(x \right)} - 1\right) \left(\tan{\left(x \right)} + 2\right) = 0$$
The graph
Sum and product of roots [src]
sum
-atan(2)
$$- \operatorname{atan}{\left(2 \right)}$$
=
-atan(2)
$$- \operatorname{atan}{\left(2 \right)}$$
product
0*(-atan(2))
$$0 \left(- \operatorname{atan}{\left(2 \right)}\right)$$
=
0
$$0$$
0
Rapid solution [src]
x1 = 0
$$x_{1} = 0$$
x2 = -atan(2)
$$x_{2} = - \operatorname{atan}{\left(2 \right)}$$
x2 = -atan(2)
Numerical answer [src]
x1 = -75.398223556983
x2 = 39.7335557788732
x3 = 100.530964793517
x4 = 25.1327420214815
x5 = 30.3087778181038
x6 = -54.5142238288206
x7 = 83.7158529291303
x8 = 56.5486676395066
x9 = -23.0982972929226
x10 = 69.1150392020375
x11 = -18.8495551574779
x12 = 77.4326676219507
x13 = 8.31762924297529
x14 = 89.9990382363099
x15 = -41.9478532144614
x16 = -69.1150386835074
x17 = -31.415926666841
x18 = 87.9645943372166
x19 = -75.398223819039
x20 = -43.9822971739403
x21 = -13.6735193321533
x22 = 12.566370609649
x23 = 31.4159269880193
x24 = -50.2654825622917
x25 = 2.0344439357957
x26 = 0.0
x27 = 18.8495560138333
x28 = 62.8318533685584
x29 = -51.3726311752308
x30 = -4.24874137138388
x31 = -31.4159264737781
x32 = -81.6814090358361
x33 = 14.6008145501549
x34 = 68.0078896611814
x35 = -48.231038521641
x36 = 74.2910749683609
x37 = -25.1327413149576
x38 = -70.2221870967695
x39 = 46.0167410860528
x40 = 50.265482194703
x41 = 58.583111700412
x42 = 80.5742602755405
x43 = -7.39033402497368
x44 = 43.9822971698479
x45 = -37.6991121875953
x46 = 33.4503704716936
x47 = 50.2654824464828
x48 = -62.8318523349934
x49 = 94.2477796093555
x50 = -85.9301503647185
x51 = 37.6991120725086
x52 = 94.2477794145545
x53 = -94.2477794152712
x54 = 18.8495567760095
x55 = -10.5319266785635
x56 = -100.530964509494
x57 = -35.6646679072818
x58 = -29.3814826001022
x59 = -50.2654822527514
x60 = 81.6814091103212
x61 = 56.548667694909
x62 = -98.4965209790777
x63 = 6.28318528482683
x64 = 96.2822235434895
x65 = -63.93900178959
x66 = 24.0255925109243
x67 = 6.2831849947568
x68 = 52.2999263932324
x69 = 36.5919631252834
x70 = 75.3982241546148
x71 = 81.6814092352823
x72 = -37.6991118758857
x73 = -87.9645943552529
x74 = -57.6558164824104
x75 = -6.28318509016395
x76 = -92.2133356718981
x77 = -56.5486673440071
x78 = -81.6814093560639
x79 = 31.4159268220714
x80 = 62.8318533022313
x81 = -12.5663701781784
x82 = -38.8062605608716
x83 = 12.5663704860339
x84 = -19.9567046393328
x85 = -79.6469650575389
x85 = -79.6469650575389