cot(pi*x/4)=1

$$cot{left (frac{pi x}{4} right )} = 1$$

Дано уравнение
$$cot{left (frac{pi x}{4} right )} = 1$$
преобразуем
$$cot{left (frac{pi x}{4} right )} – 1 = 0$$
$$cot{left (frac{pi x}{4} right )} – 1 = 0$$
Сделаем замену
$$w = cot{left (frac{pi x}{4} right )}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$w = 1$$
Получим ответ: w = 1
делаем обратную замену
$$cot{left (frac{pi x}{4} right )} = w$$
подставляем w:

$$x_{1} = 1$$

x1 = -47.0000000000000

x2 = -75.0000000000000

x3 = -19.0000000000000

x4 = -31.0000000000000

x5 = 37.0000000000000

x6 = 97.0000000000000

x7 = 29.0000000000000

x8 = -39.0000000000000

x9 = -79.0000000000000

x10 = -71.0000000000000

x11 = 73.0000000000000

x12 = 45.0000000000000

x13 = 21.0000000000000

x14 = 5.00000000000000

x15 = 25.0000000000000

x16 = -59.0000000000000

x17 = -83.0000000000000

x18 = 1.00000000000000

x19 = -63.0000000000000

x20 = 57.0000000000000

x21 = -67.0000000000000

x22 = 9.00000000000000

x23 = -11.0000000000000

x24 = -43.0000000000000

x25 = -23.0000000000000

x26 = -15.0000000000000

x27 = 89.0000000000000

x28 = 41.0000000000000

x29 = 69.0000000000000

x30 = -55.0000000000000

x31 = 81.0000000000000

x32 = 77.0000000000000

x33 = -7.00000000000000

x34 = 93.0000000000000

x35 = 17.0000000000000

x36 = -3.00000000000000

x37 = 49.0000000000000

x38 = -95.0000000000000

x39 = -99.0000000000000

x40 = 85.0000000000000

x41 = -51.0000000000000

x42 = -35.0000000000000

x43 = -87.0000000000000

x44 = -27.0000000000000

x45 = 53.0000000000000

x46 = 33.0000000000000

x47 = -91.0000000000000

x48 = 65.0000000000000

x49 = 13.0000000000000

x50 = 61.0000000000000