2sin²x/cos²x-5/cosx+4=0
cosx≠0
2sin²x-5cosx+4cos²x=0
2-2cos²x-5cosx+4cos²x=0
cosx=a
2a²-5a+2=0
D=25-16=9
a1=(5-3)/4=1/2⇒cosx=1/2⇒x=+-π/3+2πn,n∈z
3π≤-π/3+2πт≤9π/2
18≤-2+12n≤27
20≤12n≤29
5/3≤n≤29/12
n=2⇒x=-π/3+4π=11π/3
3π≤π/3+2πт≤9π/2
18≤2+12n≤27
16≤12n≤25
4/3≤n≤25/12
n=2⇒x=π/3+4π=13π/3
a2=(5+3)/4=2⇒cosx=2>1 нет решения