4*cos(2*x)-1=0

Перенесём -1 в правую часть ур-ния

с изменением знака при -1

Получим:
$$4 cos{left (2 x right )} = 1$$

Разделим обе части ур-ния на 4

Ур-ние превратится в
$$cos{left (2 x right )} = frac{1}{4}$$
Это ур-ние преобразуется в
$$2 x = pi n + {acos}{left (frac{1}{4} right )}$$
$$2 x = pi n – pi + {acos}{left (frac{1}{4} right )}$$
Или
$$2 x = pi n + {acos}{left (frac{1}{4} right )}$$
$$2 x = pi n – pi + {acos}{left (frac{1}{4} right )}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = frac{pi n}{2} + frac{1}{2} {acos}{left (frac{1}{4} right )}$$
$$x_{2} = frac{pi n}{2} – frac{pi}{2} + frac{1}{2} {acos}{left (frac{1}{4} right )}$$

acos(1/4)
x1 = pi – ———
2

acos(1/4)
x2 = ———
2

x1 = 68.4559803431000

x2 = 5.62412727135000

x3 = -21.3320905393000

x4 = 62.1727950360000

x5 = -62.1727950360000

x6 = 54.0661331469000

x7 = 98.0484302971000

x8 = -60.3493184540000

x9 = -93.5887215719000

x10 = -24.4736831929000

x11 = -16.3670213038000

x12 = -63.4909111076000

x13 = -32.0749845717000

x14 = 41.4997625325000

x15 = -54.0661331469000

x16 = 16.3670213038000

x17 = -65.3143876896000

x18 = -99.8719068790000

x19 = 90.4471289183000

x20 = 93.5887215719000

x21 = 33.8984611537000

x22 = -43.3232391144000

x23 = 25.7917992645000

x24 = 8.76571992494000

x25 = 82.3404670292000

x26 = 27.6152758465000

x27 = 0.659058035826000

x28 = 113.756393565000

x29 = -2.48253461776000

x30 = 85.4820596828000

x31 = -40.1816464608000

x32 = -11.9073125785000

x33 = -57.2077258004000

x34 = -33.8984611537000

x35 = -101.190022951000

x36 = 32.0749845717000

x37 = 40.1816464608000

x38 = 10.0838359966000

x39 = 55.8896097288000

x40 = 63.4909111076000

x41 = -82.3404670292000

x42 = 129.464356833000

x43 = -38.3581698789000

x44 = 74.7391656503000

x45 = 47.7829478397000

x46 = 66.6325037612000

x47 = -76.0572817220000

x48 = 84.1639436111000

x49 = 11748.8974664000

x50 = 60.3493184540000

x51 = -55.8896097288000

x52 = 19.5086139574000

x53 = 91.7652449899000

x54 = 46.4648317680000

x55 = 30.7568685001000

x56 = 76.0572817220000

x57 = 88.6236523363000

x58 = -41.4997625325000

x59 = 2.48253461776000

x60 = 77.8807583039000

x61 = 38.3581698789000

x62 = 71.5975729967000

x63 = -71.5975729967000

x64 = 3.80065068942000

x65 = -69.7740964148000

x66 = -13.2254286502000

x67 = 24.4736831929000

x68 = -90.4471289183000

x69 = 18.1904978857000

x70 = -3.80065068942000

x71 = -68.4559803431000

x72 = -49.6064244216000

x73 = -27.6152758465000

x74 = -98.0484302971000

x75 = 96.7303142255000

x76 = -19.5086139574000

x77 = -91.7652449899000

x78 = -18.1904978857000

x79 = -10.0838359966000

x80 = 49.6064244216000

x81 = -25.7917992645000

x82 = 44.6413551861000

x83 = 69.7740964148000

x84 = -85.4820596828000

x85 = -5.62412727135000

x86 = 11.9073125785000

x87 = -79.1988743756000

x88 = -46.4648317680000

x89 = -47.7829478397000

x90 = 52.7480170752000

x91 = -77.8807583039000

x92 = -35.2165772253000

x93 = 22.6502066110000

x94 = 99.8719068790000

x95 = -84.1639436111000