tan(2*x)=1

$$tan{left (2 x right )} = 1$$

Дано уравнение
$$tan{left (2 x right )} = 1$$
– это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = pi n + {atan}{left (1 right )}$$
Или
$$2 x = pi n + frac{pi}{4}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = frac{pi n}{2} + frac{pi}{8}$$

pi
x1 = —
8

$$x_{1} = frac{pi}{8}$$

x1 = -100.138265833000

x2 = 1.96349540849000

x3 = -31.0232274542000

x4 = 86.7864970554000

x5 = 93.0696823626000

x6 = -82.8595062384000

x7 = -73.4347282777000

x8 = -7.46128255228000

x9 = 71.0785337875000

x10 = -46.7311907221000

x11 = 88.3572933822000

x12 = -13.7444678595000

x13 = -45.1603943954000

x14 = 56.9413668463000

x15 = -1.17809724510000

x16 = -38.8772090882000

x17 = -24.7400421470000

x18 = -27.8816348006000

x19 = 60.0829594999000

x20 = 53.7997741927000

x21 = 9.81747704247000

x22 = 74.2201264411000

x23 = 12.9590696961000

x24 = 8.24668071567000

x25 = -59.2975613365000

x26 = 42.8041999052000

x27 = 96.2112750162000

x28 = -79.7179135848000

x29 = 82.0741080750000

x30 = 14.5298660229000

x31 = 5.10508806208000

x32 = -71.8639319509000

x33 = -67.1515429705000

x34 = 20.8130513300000

x35 = -29.4524311274000

x36 = -2.74889357189000

x37 = -90.7134878724000

x38 = 52.2289778659000

x39 = -95.4258768528000

x40 = 78.9325154214000

x41 = -65.5807466437000

x42 = -89.1426915456000

x43 = 67.9369411339000

x44 = -86.0010988920000

x45 = 97.7820713430000

x46 = -9.03207887907000

x47 = 31.8086256176000

x48 = 80.5033117482000

x49 = -75.0055246045000

x50 = -96.9966731796000

x51 = 64.7953484803000

x52 = -68.7223392973000

x53 = 22.3838476568000

x54 = -56.1559686829000

x55 = 0.392699081699000

x56 = -37.3064127614000

x57 = 41.2334035784000

x58 = 100.923663997000

x59 = -5.89048622548000

x60 = -57.7267650097000

x61 = 49.0873852123000

x62 = -49.8727833757000

x63 = -23.1692458202000

x64 = 19.2422550032000

x65 = 58.5121631731000

x66 = 66.3661448071000

x67 = -35.7356164346000

x68 = -21.5984494934000

x69 = -20.0276531666000

x70 = -43.5895980686000

x71 = 50.6581815391000

x72 = 94.6404786894000

x73 = -64.0099503169000

x74 = 72.6493301143000

x75 = -42.0188017418000

x76 = 36.5210145980000

x77 = -34.1648201078000

x78 = 6.67588438888000

x79 = -93.8550805260000

x80 = -51.4435797025000

x81 = 34.9502182712000

x82 = 28.6670329640000

x83 = -87.5718952188000

x84 = -12.1736715327000

x85 = 27.0962366372000

x86 = -60.8683576633000

x87 = 30.2378292908000

x88 = -16.8860605130000

x89 = 75.7909227679000

x90 = 38.0918109248000

x91 = -15.3152641863000

x92 = 23.9546439836000

x93 = 85.2157007286000

x94 = 16.1006623496000

x95 = -78.1471172580000

x96 = 44.3749962320000

x97 = 45.9457925588000

x98 = -53.0143760293000

x99 = -81.2887099116000

x100 = 89.9280897090000

x101 = 63.2245521535000