tan(2*x)=sqrt(2)/2

$$tan{left (2 x right )} = frac{sqrt{2}}{2}$$

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

/ ___
|/ 2 |
atan|—–|
2 /
x1 = ———–
2

$$x_{1} = frac{1}{2} {atan}{left (frac{sqrt{2}}{2} right )}$$

x1 = -38.9621683155000

x2 = 92.9847231352000

x3 = -82.9444654658000

x4 = 9.73251781510000

x5 = -68.8072985246000

x6 = -64.0949095443000

x7 = -37.3913719887000

x8 = -71.9488911782000

x9 = -59.3825205639000

x10 = 38.0068516974000

x11 = 67.8519819065000

x12 = 59.9980002725000

x13 = 50.5732223118000

x14 = -2.83385279925000

x15 = 49.0024259850000

x16 = -100.223225061000

x17 = 78.8475561941000

x18 = 81.9891488477000

x19 = 100.838704769000

x20 = -67.2365021978000

x21 = 12.8741104687000

x22 = 86.7015378281000

x23 = -75.0904838318000

x24 = 6.59092516151000

x25 = -45.2453536227000

x26 = -89.2276507730000

x27 = -97.0816324069000

x28 = 8.16172148831000

x29 = -81.3736691390000

x30 = 30.1528700634000

x31 = -20.1126123940000

x32 = 89.8431304816000

x33 = 75.7059635405000

x34 = 41.1484443510000

x35 = 22.2988884295000

x36 = -9.11703810643000

x37 = -56.2409279103000

x38 = 14.4449067955000

x39 = -60.9533168907000

x40 = -42.1037609691000

x41 = 63.1395929261000

x42 = 58.4272039457000

x43 = -34.2497793352000

x44 = 85.1307415013000

x45 = -49.9577426031000

x46 = 1.87853618113000

x47 = 97.6971121156000

x48 = 28.5820737366000

x49 = -27.9665940280000

x50 = -5.97544545284000

x51 = -95.5108360802000

x52 = -57.8117242371000

x53 = 5.02012883472000

x54 = -65.6657058711000

x55 = 52.1440186386000

x56 = 56.8564076190000

x57 = -16.9710197404000

x58 = 20.7280921027000

x59 = -35.8205756619000

x60 = -79.8028728122000

x61 = -87.6568544462000

x62 = 44.2900370046000

x63 = -24.8250013744000

x64 = 23.8696847563000

x65 = -29.5373903548000

x66 = 72.5643708869000

x67 = -13.8294270868000

x68 = -7.54624177964000

x69 = -15.4002234136000

x70 = 96.1263157888000

x71 = -1.26305647246000

x72 = 45.8608333314000

x73 = 64.7103892529000

x74 = -31.1081866816000

x75 = 0.307739854335000

x76 = -21.6834087208000

x77 = 36.4360553706000

x78 = -73.5196875050000

x79 = 80.4183525209000

x80 = -23.2542050476000

x81 = -93.9400397534000

x82 = 88.2723341548000

x83 = 19.1572957759000

x84 = 16.0157031223000

x85 = -46.8161499495000

x86 = -12.2586307600000

x87 = 42.7192406778000

x88 = -78.2320764854000

x89 = 34.8652590438000

x90 = 27.0112774098000

x91 = -90.7984470998000

x92 = -43.6745572959000

x93 = 31.7236663902000

x94 = -86.0860581194000

x95 = -53.0993352567000

x96 = 66.2811855797000

x97 = 94.5555194620000

x98 = 53.7148149654000

x99 = 70.9935745601000

x100 = 74.1351672137000

x101 = -51.5285389299000