ctg(2x)=1 (уравнение)

Найду корень уравнения: ctg(2x)=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 = -82.8595062384308

x2 = -92.2842841992002

x3 = -64.009950316892

x4 = -18.45685683984

x5 = -79.717913584841

x6 = 25.5254403104171

x7 = -12.1736715326604

x8 = 47.5165888855456

x9 = 36.5210145979813

x10 = -56.1559686829176

x11 = -86.0010988920206

x12 = 67.9369411338793

x13 = 45.9457925587507

x14 = -65.5807466436869

x15 = -62.4391539900971

x16 = 27.096236637212

x17 = -38.8772090881737

x18 = -21.5984494934298

x19 = -68.7223392972767

x20 = -40.4480054149686

x21 = 89.9280897090078

x22 = 38.0918109247762

x23 = 53.7997741927252

x24 = -16.8860605130451

x25 = 75.7909227678538

x26 = -60.8683576633022

x27 = -76.5763209312512

x28 = 17.6714586764426

x29 = -42.0188017417635

x30 = -29.4524311274043

x31 = 39.6626072515711

x32 = 82.0741080750334

x33 = -51.4435797025329

x34 = 52.2289778659303

x35 = 60.0829594999048

x36 = -5.89048622548086

x37 = 66.3661448070844

x38 = -7.46128255227576

x39 = 93.0696823625976

x40 = 80.5033117482384

x41 = -13.7444678594553

x42 = -20.0276531666349

x43 = 23.9546439836222

x44 = -27.8816348006094

x45 = 5.10508806208341

x46 = -78.1471172580461

x47 = -46.7311907221482

x48 = -48.3019870489431

x49 = 97.7820713429823

x50 = -49.872783375738

x51 = 22.3838476568273

x52 = 19.2422550032375

x53 = -35.7356164345839

x54 = 14.5298660228528

x55 = 30.2378292908018

x56 = -98.5674695063798

x57 = 83.6449044018282

x58 = -43.5895980685584

x59 = 16.1006623496477

x60 = -87.5718952188155

x61 = 69.5077374606742

x62 = 1.96349540849362

x63 = 9.8174770424681

x64 = 96.2112750161874

x65 = 41.233403578366

x66 = -10.6028752058656

x67 = -32.5940237809941

x68 = 61.6537558266997

x69 = 88.3572933822129

x70 = -70.2931356240716

x71 = -90.7134878724053

x72 = 8.24668071567321

x73 = -75.0055246044563

x74 = -4.31968989868597

x75 = 99.3528676697772

x76 = 71.0785337874691

x77 = 55.3705705195201

x78 = -54.5851723561227

x79 = 63.2245521534946

x80 = -26.3108384738145

x81 = -57.7267650097125

x82 = -71.8639319508665

x83 = 31.8086256175967

x84 = -84.4303025652257

x85 = 44.3749962319558

x86 = -93.8550805259951

x87 = 85.2157007286231

x88 = -24.7400421470196

x89 = -96.9966731795849

x90 = 11.388273369263

x91 = 49.0873852123405

x92 = 91.4988860358027

x93 = 74.2201264410589

x94 = 33.3794219443916

x95 = 58.5121631731099

x96 = 77.3617190946487

x97 = -34.164820107789

x98 = 3.53429173528852

x99 = -2.74889357189107

x100 = -100.138265833175

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