7*cos(2*x+1)=2

Разделим обе части ур-ния на 7

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

1 acos(2/7)
x1 = – – + ———
2 2

1 acos(2/7)
x2 = – – + pi – ———
2 2

x1 = -65.8329234127000

x2 = 100.671487228000

x3 = 64.8329234127000

x4 = 15.8484855806000

x5 = 94.3883019204000

x6 = 23.9922189160000

x7 = 89.9656646414000

x8 = -85.9635239596000

x9 = -6.14266299450000

x10 = -43.8417748376000

x11 = 52.2665527983000

x12 = 81.8219313060000

x13 = -57.6891900773000

x14 = 61.6913307591000

x15 = -48.2644121165000

x16 = -4.28211496627000

x17 = -51.4060047701000

x18 = 20.8506262624000

x19 = -73.3971533452000

x20 = 96.2488499486000

x21 = -28.1338115696000

x22 = -1.14052231268000

x23 = 42.8417748376000

x24 = -13.7068929270000

x25 = 67.9745160663000

x26 = 74.2577013735000

x27 = 59.8307827309000

x28 = -50.1249601448000

x29 = 88.1051166132000

x30 = -87.8240719878000

x31 = 0.140522312679000

x32 = 28.4148561950000

x33 = 83.6824793342000

x34 = -94.1072572950000

x35 = -100.390442602000

x36 = 53.5475974237000

x37 = -79.6803386524000

x38 = -12.4258483017000

x39 = -21.8506262624000

x40 = 97.5298945740000

x41 = 2.00107034091000

x42 = -15.5674409553000

x43 = 80.5408866807000

x44 = 22.1316708878000

x45 = 58.5497381055000

x46 = -19.9900782342000

x47 = -92.2467092668000

x48 = 31.5564488486000

x49 = -7.42370761986000

x50 = -63.9723753845000

x51 = 72.3971533452000

x52 = -95.3883019204000

x53 = -70.2555606917000

x54 = 30.2754042232000

x55 = 45.9833674912000

x56 = 3.28211496627000

x57 = 17.7090336089000

x58 = 39.7001821840000

x59 = -59.5497381055000

x60 = 86.8240719878000

x61 = 9.56530027345000

x62 = 44.1228194629000

x63 = 8.28425564809000

x64 = -81.5408866807000

x65 = -37.5585895304000

x66 = 36.5585895304000

x67 = 37.8396341558000

x68 = 66.1139680381000

x69 = 50.4060047701000

x70 = 75.5387459988000

x71 = -26.2732635414000

x72 = -34.4169968768000

x73 = -72.1161087199000

x74 = -29.4148561950000

x75 = -56.4081454519000

x76 = -35.6980415022000

x77 = -90.9656646414000

x78 = 6.42370761986000

x79 = 14.5674409553000

x80 = 159.080703020000

x81 = -41.9812268093000

x82 = -78.3992940271000