cot(2*x)-1=0 (уравнение)

Найду корень уравнения: cot(2*x)-1=0

Вы ввели

cot(2*x) - 1 = 0

$$\cot{\left(2 x \right)} - 1 = 0$$

Подробное решение

Дано уравнение
$$\cot{\left(2 x \right)} - 1 = 0$$
преобразуем
$$\cot{\left(2 x \right)} - 1 = 0$$
$$\left(\cot{\left(2 x \right)} - 1\right) + 0 = 0$$
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 = -68.7223392972767

x2 = -79.717913584841

x3 = -86.0010988920206

x4 = 60.0829594999048

x5 = -51.4435797025329

x6 = 23.9546439836222

x7 = -42.0188017417635

x8 = 38.0918109247762

x9 = -2.74889357189107

x10 = 27.096236637212

x11 = -40.4480054149686

x12 = -75.0055246044563

x13 = -82.8595062384308

x14 = 3.53429173528852

x15 = -71.8639319508665

x16 = 75.7909227678538

x17 = 91.4988860358027

x18 = -54.5851723561227

x19 = 47.5165888855456

x20 = 45.9457925587507

x21 = -32.5940237809941

x22 = -5.89048622548086

x23 = 77.3617190946487

x24 = -62.4391539900971

x25 = 99.3528676697772

x26 = -12.1736715326604

x27 = -34.164820107789

x28 = -46.7311907221482

x29 = 33.3794219443916

x30 = 9.8174770424681

x31 = -49.872783375738

x32 = 96.2112750161874

x33 = 55.3705705195201

x34 = 66.3661448070844

x35 = -100.138265833175

x36 = -60.8683576633022

x37 = -38.8772090881737

x38 = -18.45685683984

x39 = -93.8550805259951

x40 = 11.388273369263

x41 = 61.6537558266997

x42 = -84.4303025652257

x43 = 80.5033117482384

x44 = 85.2157007286231

x45 = 88.3572933822129

x46 = 36.5210145979813

x47 = -76.5763209312512

x48 = -70.2931356240716

x49 = -21.5984494934298

x50 = -57.7267650097125

x51 = 82.0741080750334

x52 = -87.5718952188155

x53 = -64.009950316892

x54 = 83.6449044018282

x55 = -26.3108384738145

x56 = 14.5298660228528

x57 = 89.9280897090078

x58 = 22.3838476568273

x59 = 5.10508806208341

x60 = 17.6714586764426

x61 = 52.2289778659303

x62 = 97.7820713429823

x63 = -98.5674695063798

x64 = 8.24668071567321

x65 = -92.2842841992002

x66 = 31.8086256175967

x67 = 93.0696823625976

x68 = 19.2422550032375

x69 = -20.0276531666349

x70 = 39.6626072515711

x71 = -16.8860605130451

x72 = -35.7356164345839

x73 = -7.46128255227576

x74 = 67.9369411338793

x75 = -27.8816348006094

x76 = -10.6028752058656

x77 = 58.5121631731099

x78 = -13.7444678594553

x79 = -24.7400421470196

x80 = 69.5077374606742

x81 = -78.1471172580461

x82 = 41.233403578366

x83 = 49.0873852123405

x84 = -29.4524311274043

x85 = 63.2245521534946

x86 = -4.31968989868597

x87 = -43.5895980685584

x88 = 44.3749962319558

x89 = 30.2378292908018

x90 = -48.3019870489431

x91 = -65.5807466436869

x92 = -96.9966731795849

x93 = 25.5254403104171

x94 = 71.0785337874691

x95 = -56.1559686829176

x96 = -90.7134878724053

x97 = 74.2201264410589

x98 = 53.7997741927252

x99 = 1.96349540849362

x100 = 16.1006623496477

График