Замена tg² x=y
ctg² x= 1/y
3y + 1/y =4
y≠0
3y² +1 -4y=0
3y²-4y+1=0
D=16-12=4
y₁= 4-2 = 2/6 = 1/3
6
y₂= 4+2 =1
6
При у=1/3:
tg² x=1/3
1) tgx=1/√3
x=π/6 +πk, k∈Z
2) tgx= -1/√3
x= -π/6 +πk, k∈Z
При у=1
tg² x=1
1) tgx=1
x=π/4 +πk, k∈Z
2) tgx= -1
x= -π/4 +πk, k∈Z
Ответ: + π/6 +πk, k∈Z;
+ π/4+πk, k∈Z.