Mister Exam

tg(x)(ctg(x)-cos(x))=2sin(2x)^2 equation

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Numerical solution:

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The solution

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                                2
tan(x)*(cot(x) - cos(x)) = 2*sin (2*x)
$$\left(- \cos{\left(x \right)} + \cot{\left(x \right)}\right) \tan{\left(x \right)} = 2 \sin^{2}{\left(2 x \right)}$$
The graph
Sum and product of roots [src]
sum
0
$$0$$
=
0
$$0$$
product
1
$$1$$
=
1
$$1$$
1
x1 = 75.712382951514
x2 = -13.0899693899575
x3 = 68.1725605828985
x4 = 1.57079642323511
x5 = -83.8805238508475
x6 = -31.9395253114962
x7 = -34.0339204138894
x8 = 4.08407044966673
x9 = -61.2610564700665
x10 = -46.6002910282486
x11 = 34.2433599241287
x12 = 84.5088423815654
x13 = 45.553093441597
x14 = -5.96902604182061
x15 = -97.7035315266426
x16 = -54.9778711811089
x17 = 70.6858347066598
x18 = 41.7831822927443
x19 = -100.216805649514
x20 = 60.2138591938044
x21 = -60.0044196835651
x22 = 44.2964564156161
x23 = -73.8274272809227
x24 = -9.73893722612836
x25 = 26.7035376165518
x26 = -86.3937979007636
x27 = 64.402649315709
x28 = 53.9306738866248
x29 = 5.34070751110265
x30 = -63.7743308678728
x31 = 95.8185760408313
x32 = 16.2315620435473
x33 = 78.2256570743859
x34 = -53.7212343763855
x35 = -87.6504350351552
x36 = 92.0486647501809
x37 = -82.2050077689329
x38 = -93.9336203423348
x39 = -13.5088484104361
x40 = 81.9955682586936
x41 = -33.6150413934108
x42 = 62.3082542961976
x43 = -67.5442421525188
x44 = 38.0132711084365
x45 = -29.8451301004081
x46 = 1.57079634265433
x47 = 40.5265452313083
x48 = 89.5353905135251
x49 = 24.1902634326414
x50 = 48.0663675999238
x51 = -39.8982267005904
x52 = 14.1371670741504
x53 = -46.18141200777
x54 = -80.1106125860317
x55 = 74.4557458900781
x56 = 30.473448739821
x57 = -75.9218224617533
x58 = 182.526533173567
x59 = 22.9336263712055
x60 = -2.19911485751286
x61 = -70.0575161750524
x62 = 7.85398172911943
x63 = -12.2522113490002
x64 = 20.4203521589613
x65 = -214.151899219704
x66 = -36.128315428008
x67 = -90.1637091580271
x68 = -17.2787594419908
x69 = -27.7507351067098
x70 = 51.8362788853931
x71 = -38.2227106186758
x72 = -42.4115007735831
x73 = 100.007366139275
x74 = -56.2345084992573
x75 = -47.4380490692059
x76 = -49.9513231920777
x77 = -78.0162175641465
x78 = 49.3230046613598
x79 = -43.6681378848981
x80 = 12.0427718387609
x81 = 58.1194638203606
x82 = -6.80678408277789
x83 = 27.9601746169492
x84 = 85.7654794430014
x85 = -57.4911455606932
x86 = -71.733032256967
x87 = 66.9159235214626
x88 = 9.94837673636768
x89 = 88.2787535658732
x90 = -16.0221225333079
x91 = 564.544199850086
x92 = 31.7300858012569
x93 = 71.9424717672063
x94 = -23.5619449971286
x95 = -19.7920337176157
x96 = 56.025068989018
x96 = 56.025068989018