Question

решите уравнение (2cos^2x-3cosx+1)кореньctgx=0

Answer 1

ОДЗ
ctgx≥0⇒x∈[πn,π/2+πn,n∈z]
2cos²x-3cosx+1=0
cosx=a
2a²-3a+1=0
D=9-8=1
a1=(3+1)/4=1⇒cosx=1⇒x=2πn+ОДЗ⇒х=2πn.n∈z
a2=(3-1)/4=1/2⇒cosx=+-π/6+2πn+ОДЗ⇒х=+-π/6+2πn