2*cos(3*x)=sqrt(3)

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$cos{left (3 x right )} = frac{sqrt{3}}{2}$$
Это ур-ние преобразуется в
$$3 x = pi n + {acos}{left (frac{sqrt{3}}{2} right )}$$
$$3 x = pi n – pi + {acos}{left (frac{sqrt{3}}{2} right )}$$
Или
$$3 x = pi n + frac{pi}{6}$$
$$3 x = pi n – frac{5 pi}{6}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = frac{pi n}{3} + frac{pi}{18}$$
$$x_{2} = frac{pi n}{3} – frac{5 pi}{18}$$

pi
x1 = —
18

11*pi
x2 = —–
18

x1 = 62.6573201466000

x2 = 46.2512251778000

x3 = -6.10865238198000

x4 = 6.10865238198000

x5 = 73.1292956586000

x6 = 31.5904594611000

x7 = 56.3741348394000

x8 = 98.2620368873000

x9 = 12.3918376892000

x10 = 18.6750229963000

x11 = 83.9503370209000

x12 = 8.20304748437000

x13 = -22.8638132011000

x14 = -10.6465084372000

x15 = -58.4685299418000

x16 = 96.1676417849000

x17 = -52.1853446346000

x18 = -79.4124809657000

x19 = -73.4783615090000

x20 = 52.1853446346000

x21 = 27.0526034059000

x22 = 88.1391272257000

x23 = -79.7615468161000

x24 = 64.7517152490000

x25 = 16.5806278939000

x26 = -60.9119908946000

x27 = -27.4016692563000

x28 = -50.0909495322000

x29 = 81.8559419185000

x30 = 50.0909495322000

x31 = 14.4862327916000

x32 = -1.91986217719000

x33 = 29.4960643587000

x34 = -47.9965544298000

x35 = -33.6848545635000

x36 = -29.4960643587000

x37 = 47.9965544298000

x38 = -25.3072741539000

x39 = -56.3741348394000

x40 = 0.174532925199000

x41 = -69.2895713042000

x42 = 91.9788515801000

x43 = 10.2974425868000

x44 = 4.01425727959000

x45 = -75.5727566114000

x46 = 42.0624349731000

x47 = -41.7133691227000

x48 = -8.20304748437000

x49 = 2.26892802759000

x50 = -10.2974425868000

x51 = 79.7615468161000

x52 = 54.2797397370000

x53 = -14.4862327916000

x54 = -96.1676417849000

x55 = -91.9788515801000

x56 = 94.0732466825000

x57 = 37.8736447683000

x58 = -37445.8645686000

x59 = 75.5727566114000

x60 = -86.0447321233000

x61 = -94.0732466825000

x62 = -98.2620368873000

x63 = -66.8461103514000

x64 = -20.7694180987000

x65 = 29.1469985083000

x66 = -12.3918376892000

x67 = 35.7792496659000

x68 = 39.9680398707000

x69 = -31.5904594611000

x70 = 8763.12364134000

x71 = 60.5629250442000

x72 = 67.1951762018000

x73 = 90.2335223281000

x74 = -81.5068760681000

x75 = -39.9680398707000

x76 = 44.1568300755000

x77 = -89.8844564777000

x78 = -83.9503370209000

x79 = 33.6848545635000

x80 = -71.3839664066000

x81 = 100.356431990000

x82 = 16.9296937443000

x83 = 86.0447321233000

x84 = -100.356431990000

x85 = -54.2797397370000

x86 = -43.8077642251000

x87 = -4.01425727959000

x88 = -37.8736447683000

x89 = 77.6671517137000

x90 = -16.9296937443000

x91 = 100.705497840000

x92 = -87.7900613753000

x93 = -81.8559419185000

x94 = -35.7792496659000

x95 = 25.3072741539000

x96 = 58.4685299418000

x97 = -45.9021593275000

x98 = -77.6671517137000