cos(2*x)=sin(2*x)

$$cos{left (2 x right )} = sin{left (2 x right )}$$

Дано уравнение
$$cos{left (2 x right )} = sin{left (2 x right )}$$
преобразуем:
$$- frac{sin{left (2 x right )}}{cos{left (2 x right )}} = -1$$
или
$$- tan{left (2 x right )} = -1$$
– это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$tan{left (2 x right )} = -1$$
Это ур-ние преобразуется в
$$2 x = pi n + {atan}{left (-1 right )}$$
Или
$$2 x = pi n – frac{pi}{4}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = frac{pi n}{2} – frac{pi}{8}$$

-3*pi
x1 = —–
8

$$x_{1} = – frac{3 pi}{8}$$

pi
x2 = —
8

$$x_{2} = frac{pi}{8}$$

x1 = -100.138265833000

x2 = 1.96349540849000

x3 = 74.2201264411000

x4 = 39.6626072516000

x5 = 47.5165888855000

x6 = -78.1471172580000

x7 = -26.3108384738000

x8 = 8.24668071567000

x9 = -59.2975613365000

x10 = 66.3661448071000

x11 = 96.2112750162000

x12 = -93.8550805260000

x13 = 69.5077374607000

x14 = 23.9546439836000

x15 = -79.7179135848000

x16 = -51.4435797025000

x17 = -15.3152641863000

x18 = -56.1559686829000

x19 = -84.4303025652000

x20 = 91.4988860358000

x21 = -4.31968989869000

x22 = 82.0741080750000

x23 = 28.6670329640000

x24 = -70.2931356241000

x25 = -118.987821755000

x26 = -42.0188017418000

x27 = 67.9369411339000

x28 = -12.1736715327000

x29 = -40.4480054150000

x30 = -18.4568568398000

x31 = -57.7267650097000

x32 = -13.7444678595000

x33 = -20.0276531666000

x34 = -29.4524311274000

x35 = 22.3838476568000

x36 = -5.89048622548000

x37 = -62.4391539901000

x38 = 83.6449044018000

x39 = -49.8727833757000

x40 = 0.392699081699000

x41 = 88.3572933822000

x42 = -92.2842841992000

x43 = 17.6714586764000

x44 = 61.6537558267000

x45 = 94.6404786894000

x46 = 52.2289778659000

x47 = -95.4258768528000

x48 = 30.2378292908000

x49 = -65.5807466437000

x50 = -2801.90794792000

x51 = 38.0918109248000

x52 = 58.5121631731000

x53 = 14.5298660229000

x54 = 89.9280897090000

x55 = -73.4347282777000

x56 = 16.1006623496000

x57 = -21.5984494934000

x58 = 25.5254403104000

x59 = -86.0010988920000

x60 = 97.7820713430000

x61 = 44.3749962320000

x62 = -43.5895980686000

x63 = -71.8639319509000

x64 = 3.53429173529000

x65 = 50.6581815391000

x66 = -87.5718952188000

x67 = -7.46128255228000

x68 = 31.8086256176000

x69 = -64.0099503169000

x70 = -27.8816348006000

x71 = 60.0829594999000

x72 = -81.2887099116000

x73 = 72.6493301143000

x74 = -37.3064127614000

x75 = 53.7997741927000

x76 = 9.81747704247000

x77 = -35.7356164346000

x78 = -48.3019870489000

x79 = 45.9457925588000

x80 = 6.67588438888000

x81 = 75.7909227679000

x82 = 36.5210145980000

x83 = 80.5033117482000

x84 = -34.1648201078000

x85 = -32.5940237810000