Question

Ctgx+1/sin^2x=3 ctgx по модулю

Answer 1

Ctgx +1/sin²x=3/ctgx/
1/sin²x=ctg²x+1
ctg²x+ctgx+1=3/ctgx/
1)ctgx<0⇒x∈(π/2;π)
ctg²x+ctgx+1=-3ctgx
ctg²x+4ctgx+1=0
ctgx=a
a²+4a+1=0
D=16-4=12
a1=-2-√2⇒ctgx=-2-√2⇒x=-arcctg(2+√2)+πn
a2=-2+√2⇒ctgx=-2+√2⇒x=arcctg(-2+√2)+πn
2)ctgx≥0⇒x∈(0;π/2]
ctg²x+ctgx+1=3ctgx
ctg²x-2ctgx+1=0
(ctgx-1)²=0
ctgx=1⇒x=π/4