Verified answer

ctg(x/2) - tg(x/2) - 2*tg(x) = 4

(1+cosx)/(sinx) - (1-cosx)/(sinx) - 2 * sinx/cosx = 4

(1+cosx-1+cosx)/(sinx) - 2*sinx/cosx =4

2*(cos²x - sin²x)/(sinx*cosx)=4

2*cos(2x)/(2sinx*cosx)=2

ctg(2x)=1

2x = π/4 + πn, n ∈ Z

x = π/8 + π*n/2, n ∈ Z

Ответ: π/8 + π*n/2, n ∈ Z

Формулы:

ctg(x/2) = (1+cosx)/sinx

tg(x/2) = (1-cosx)/sinx

sin 2x = 2sinx*cosx

cos 2x = cos²x - sin²x

ctg(x) = a

x = arcctg(a) + πn, n ∈ Z