Tg(x + π/3) + 3Ctg(x +π/3) = 4
tg(x + π/3) + 3/tg(x +π/3) = 4
tg(x + π/3) = y
y +3/y = 4|* y
y² +3 = 4y
y² -4y +3 = 0
по т. Виета корни будут 1 и 3
а)у = 1
tg(x +π/3) = 1
x + π/3 = arctg1 + πk , k ∈ Z
x = -π/3 + π/4 + πk , k ∈ Z
x = π/12 + πk , k ∈Z
б) y = 3
tg(x + π/3) = 3
x + π/3 = arctg3 + πn , n∈Z
x = -π/3 + arctg3 + πn , n ∈Z