2*sin(2*x)-1=0

Перенесём -1 в правую часть ур-ния

с изменением знака при -1

Получим:
$$2 sin{left (2 x right )} = 1$$

Разделим обе части ур-ния на 2

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

pi
x1 = —
12

5*pi
x2 = —-
12

x1 = 15.9697626557000

x2 = -42.6733002113000

x3 = 6.54498469498000

x4 = -64.6644487864000

x5 = -1.83259571459000

x6 = -45.8148928649000

x7 = 51.5744793964000

x8 = -65.7116463376000

x9 = -30.1069295969000

x10 = 13.8753675534000

x11 = 78.8016157275000

x12 = -31.1541271481000

x13 = -67.8060414400000

x14 = -694.030177056000

x15 = -9.16297857297000

x16 = -50.0036830696000

x17 = 95.5567765467000

x18 = 45.2912940893000

x19 = 20.1585528605000

x20 = -56.2868683768000

x21 = 64.1408500108000

x22 = 48.4328867428000

x23 = 86.1319985859000

x24 = 50.5272818452000

x25 = -6.02138591938000

x26 = 12.8281700022000

x27 = -100.269165527000

x28 = 70.4240353180000

x29 = -39.5317075577000

x30 = 72.5184304204000

x31 = -28.0125344945000

x32 = 57.8576647036000

x33 = 28.5361332701000

x34 = -53.1452757232000

x35 = 29.5833308213000

x36 = 35.8665161285000

x37 = 0.261799387799000

x38 = -23.8237442897000

x39 = 73.5656279716000

x40 = 42.1497014357000

x41 = -52.0980781720000

x42 = -17.5405589825000

x43 = 92.4151838931000

x44 = -61.5228561328000

x45 = -96.0803753223000

x46 = -86.6555973615000

x47 = 34.8193185773000

x48 = -93.9859802199000

x49 = 4.45058959259000

x50 = -12.3045712266000

x51 = -8.11578102177000

x52 = 66.2352451132000

x53 = -43.7204977625000

x54 = -21.7293491873000

x55 = 59.9520598060000

x56 = -75.1364242984000

x57 = -36.3901149041000

x58 = -59.4284610304000

x59 = -80.3724120543000

x60 = 26.4417381677000

x61 = -78.2780169519000

x62 = 7.59218224618000

x63 = -55.2396708256000

x64 = 22.2529479629000

x65 = -87.7027949127000

x66 = -40.5789051089000

x67 = -97.1275728735000

x68 = 53.6688744988000

x69 = 79.8488132787000

x70 = -89.7971900151000

x71 = -71.9948316448000

x72 = -83.5140047079000

x73 = 94.5095789955000

x74 = -74.0892267472000

x75 = -58.3812634792000

x76 = 31.6777259237000

x77 = -14.3989663290000

x78 = -81.4196096055000

x79 = 56.8104671524000

x80 = 100.792764303000

x81 = -37.4373124553000

x82 = 37.9609112309000

x83 = 75.6600230740000

x84 = -15.4461638801000

x85 = -34.2957198017000

x86 = 81.9432083811000

x87 = 88.2263936883000

x88 = 44.2440965381000

x89 = 9.68657734857000