2*cos(5*x-pi/4)=1

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$sin{left (5 x + frac{pi}{4} right )} = frac{1}{2}$$
Это ур-ние преобразуется в
$$5 x + frac{pi}{4} = 2 pi n + {asin}{left (frac{1}{2} right )}$$
$$5 x + frac{pi}{4} = 2 pi n – {asin}{left (frac{1}{2} right )} + pi$$
Или
$$5 x + frac{pi}{4} = 2 pi n + frac{pi}{6}$$
$$5 x + frac{pi}{4} = 2 pi n + frac{5 pi}{6}$$
, где n – любое целое число
Перенесём
$$frac{pi}{4}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$5 x = 2 pi n – frac{pi}{12}$$
$$5 x = 2 pi n + frac{7 pi}{12}$$
Разделим обе части полученного ур-ния на
$$5$$
получим ответ:
$$x_{1} = frac{2 pi}{5} n – frac{pi}{60}$$
$$x_{2} = frac{2 pi}{5} n + frac{7 pi}{60}$$

-pi
x1 = —-
60

7*pi
x2 = —-
60

x1 = 90.4255085458000

x2 = -5.91666616426000

x3 = 92.1010246277000

x4 = 6.23082542962000

x5 = 68.2249204605000

x6 = 20.0538331054000

x7 = -27.6983752292000

x8 = 40.1600260884000

x9 = 14.1895268187000

x10 = -56.1821486217000

x11 = 48.1187274775000

x12 = -33.9815605363000

x13 = 2.87979326579000

x14 = -70.0051562975000

x15 = -27.2794962087000

x16 = -26.0228591472000

x17 = 85.8178393206000

x18 = 74.0892267472000

x19 = -63.7219709903000

x20 = 30.1069295969000

x21 = -47.8045682121000

x22 = 16.2839219211000

x23 = -12.1998514714000

x24 = -93.8812604648000

x25 = 61.5228561328000

x26 = -3.82227106187000

x27 = 60.2662190714000

x28 = -39.8458668230000

x29 = -7.59218224618000

x30 = 38.0656309860000

x31 = 53.9830337642000

x32 = -37.7514717206000

x33 = -446.158516687000

x34 = -41.1025038845000

x35 = -19.7396738401000

x36 = 80.3724120543000

x37 = 82.0479281363000

x38 = -83.8281639733000

x39 = -81.7337688709000

x40 = 24.2426233102000

x41 = 71.9948316448000

x42 = -88.0169541781000

x43 = -15.9697626557000

x44 = -13.8753675534000

x45 = -0.0523598775598000

x46 = -23.9284640448000

x47 = -9.68657734857000

x48 = -73.7750674818000

x49 = 26.3370184126000

x50 = 95.8709358120000

x51 = -92.6246234033000

x52 = -46.1290521302000

x53 = 97.9653309144000

x54 = -44.0346570278000

x55 = 7.90634151153000

x56 = -36.0759556387000

x57 = 50.2131225799000

x58 = 34.2957198017000

x59 = 36.3901149041000

x60 = -2.14675497995000

x61 = 100.897484058000

x62 = 64.0361302557000

x63 = 46.4432113956000

x64 = 84.1423232386000

x65 = -51.5744793964000

x66 = -57.8576647036000

x67 = 31.3635666583000

x68 = -77.9638576866000

x69 = -100.164445772000

x70 = -71.6806723794000

x71 = 10.0007366139000

x72 = 70.3193155629000

x73 = 94.1954197301000

x74 = -29.7927703315000

x75 = 4.13643032723000

x76 = 78.2780169519000

x77 = -95.5567765467000

x78 = -59.9520598060000

x79 = 13.7706477982000

x80 = -17.6452787377000

x81 = -67.9107611951000

x82 = 51.8886386618000

x83 = 41.8355421703000

x84 = 28.0125344945000

x85 = -49.8989633145000

x86 = 17.9594380030000

x87 = 251.275052410000

x88 = -90.1113492805000

x89 = -91.7868653624000

x90 = 61.9417351533000

x91 = -80.0582527890000

x92 = -61.6275758879000

x93 = 58.1718239690000

x94 = 43.0921792317000