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
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