Step-by-step explanation:
cosec²x = 1/sin²x = (sin²x+cos²x)/sin²x =1 + cos²x/sin²x = 1 + cot²x.
Therefore:
1+cot²x = 3cot x - 1
cot²x - 3 cot x + 2 = 0
let cot x = t
t²-3t+2=0
t²-2t-t+2=0
t(t-2)-(t-2)=0
(t-1)(t-2)=0
t1=1
t2=2
so:
cot x = 1 then x1 = π/4 + πk
cot x = 2 then x2 = arccot(2) + πk
k is an integral.
