1
сos²x/sin²x+3/sinx+3=0
sinx≠0
1-sin²x+3sinx+3sin²x=0
sinx=a
2a²+3a+1=0
D=9-8=1
a1=(-3-1)/4=-1⇒sinx=-1⇒x=-π/2+2πn,n∈z
2π≤-π/2+2πn≤7π/2
4≤-1+4n≤7
5≤4n≤8
5/4≤n≤2
n=2⇒x=-π/2+4π=7π/2
a2=(-3+10/4=-1/2⇒sinx=-1/2
x=-π/6+2πk,k∈z U x=7π/6+2πm,m∈z
2π≤-π/6+2πk≤7π/2
12≤-1+12k≤21
13≤12k≤22
13/12≤k≤11/6
нет решения
2π≤7π/6+2πm≤7π/2
12≤7+12m≤21
5≤12m≤14
5/12≤m≤14/12
m=1⇒x=7π/6+2π=16π/6
2
sinx≠0
2sin²x-sinx-1=0
sinx=a
2a²-a-1=0
D=1+8=9
a1=(1-3)/4=-1/2⇒sinx=-1/2
x=-π/6+2πk,k∈z U x=7π/6+2πm,m∈z
π≤-π/6+2πk≤5π/2
6≤-1+12k≤15
7≤12k≤16
7/12≤k≤4/3
k=1⇒x=-π/6+2π=11π/6
π≤7π+2πm≤5π/2
6≤7+12m≤15
-1≤12m≤8
-1/12≤m≤2/3
m=0⇒x=7π/6
a2=(1+3)/4=1⇒sinx=1⇒x=π/2+2πn,n∈z
π≤π/2+2πn≤5π/2
2≤1+4n≤5
1≤4n≤4
1/4≤n≤1
n=1⇒x=π/2+2π=5π/2