cot(x/2)=1

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

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

pi
x1 = —
2

$$x_{1} = frac{pi}{2}$$

x1 = -54.9778714378000

x2 = -17.2787595947000

x3 = 45.5530934771000

x4 = 83.2522053201000

x5 = -4.71238898038000

x6 = 76.9690200129000

x7 = -48.6946861306000

x8 = -80.1106126665000

x9 = -42.4115008235000

x10 = 58.1194640914000

x11 = 39.2699081699000

x12 = 95.8185759345000

x13 = -36.1283155163000

x14 = -92.6769832809000

x15 = 32.9867228627000

x16 = 7.85398163397000

x17 = 51.8362787842000

x18 = 64.4026493986000

x19 = -73.8274273594000

x20 = 14.1371669412000

x21 = 26.7035375555000

x22 = -98.9601685881000

x23 = -67.5442420522000

x24 = 1.57079632679000

x25 = -61.2610567450000

x26 = -86.3937979737000

x27 = 89.5353906273000

x28 = -10.9955742876000

x29 = -23.5619449019000

x30 = 70.6858347058000

x31 = 20.4203522483000

x32 = -29.8451302091000