ctg2x=1 (уравнение)

Найду корень уравнения: ctg2x=1

Вы ввели

cot(2*x) = 1

$$\cot{\left(2 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\cot{\left(2 x \right)} = 1$$
преобразуем
$$\cot{\left(2 x \right)} - 1 = 0$$
$$\cot{\left(2 x \right)} - 1 = 0$$
Сделаем замену
$$w = \cot{\left(2 x \right)}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$w = 1$$
Получим ответ: w = 1
делаем обратную замену
$$\cot{\left(2 x \right)} = w$$
подставляем w:

Быстрый ответ

     pi
x1 = --
     8 

$$x_{1} = \frac{\pi}{8}$$

Сумма и произведение корней

сумма

    pi
0 + --
    8 

$$0 + \frac{\pi}{8}$$

=

pi
--
8 

$$\frac{\pi}{8}$$

произведение

  pi
1*--
  8 

$$1 \frac{\pi}{8}$$

=

pi
--
8 

$$\frac{\pi}{8}$$

Численный ответ

x1 = 5.10508806208341

x2 = 83.6449044018282

x3 = 66.3661448070844

x4 = -92.2842841992002

x5 = -71.8639319508665

x6 = -62.4391539900971

x7 = -5.89048622548086

x8 = 33.3794219443916

x9 = 3.53429173528852

x10 = -79.717913584841

x11 = 96.2112750161874

x12 = -96.9966731795849

x13 = -93.8550805259951

x14 = -21.5984494934298

x15 = -75.0055246044563

x16 = -68.7223392972767

x17 = 88.3572933822129

x18 = 58.5121631731099

x19 = -100.138265833175

x20 = 30.2378292908018

x21 = 17.6714586764426

x22 = -13.7444678594553

x23 = 99.3528676697772

x24 = 85.2157007286231

x25 = 60.0829594999048

x26 = -87.5718952188155

x27 = 91.4988860358027

x28 = 39.6626072515711

x29 = -60.8683576633022

x30 = -26.3108384738145

x31 = 52.2289778659303

x32 = -2.74889357189107

x33 = -90.7134878724053

x34 = -48.3019870489431

x35 = 47.5165888855456

x36 = 63.2245521534946

x37 = 82.0741080750334

x38 = 36.5210145979813

x39 = -24.7400421470196

x40 = 31.8086256175967

x41 = 77.3617190946487

x42 = -78.1471172580461

x43 = -18.45685683984

x44 = 38.0918109247762

x45 = -82.8595062384308

x46 = 74.2201264410589

x47 = -70.2931356240716

x48 = -46.7311907221482

x49 = 22.3838476568273

x50 = 55.3705705195201

x51 = -10.6028752058656

x52 = 8.24668071567321

x53 = 53.7997741927252

x54 = -43.5895980685584

x55 = 41.233403578366

x56 = 14.5298660228528

x57 = -16.8860605130451

x58 = 44.3749962319558

x59 = -98.5674695063798

x60 = 67.9369411338793

x61 = -38.8772090881737

x62 = 69.5077374606742

x63 = 19.2422550032375

x64 = -4.31968989868597

x65 = 1.96349540849362

x66 = -32.5940237809941

x67 = -20.0276531666349

x68 = -35.7356164345839

x69 = -56.1559686829176

x70 = 27.096236637212

x71 = -64.009950316892

x72 = 80.5033117482384

x73 = 11.388273369263

x74 = 61.6537558266997

x75 = -42.0188017417635

x76 = -51.4435797025329

x77 = 97.7820713429823

x78 = -76.5763209312512

x79 = -65.5807466436869

x80 = -54.5851723561227

x81 = 9.8174770424681

x82 = 45.9457925587507

x83 = 16.1006623496477

x84 = -29.4524311274043

x85 = -57.7267650097125

x86 = -84.4303025652257

x87 = -27.8816348006094

x88 = 89.9280897090078

x89 = 49.0873852123405

x90 = -7.46128255227576

x91 = 23.9546439836222

x92 = -34.164820107789

x93 = -40.4480054149686

x94 = -12.1736715326604

x95 = 71.0785337874691

x96 = 25.5254403104171

x97 = -49.872783375738

x98 = -86.0010988920206

x99 = 75.7909227678538

x100 = 93.0696823625976

График