ОДЗ
1)sinx>0⇒2πn2)sinx≠1⇒x≠π/2+2πn,n∈z
3)cos2x-sinx+1>0
1-2sin²x-sinx+1>0
2sin²x+sinx-2<0<br>sinx=a
2a²+a-2<0<br>D=1+16=17
a1=(-1-√17)/4 U a2=(-1+√17)/4
(-1-√17)/4-π/2+2πnx∈(2πn;arcsin(-1+√17)/4+2πn,n∈z) U (arcsin(-1+√17)/4+2πn;π+2πn,n∈z)
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cos2x-sinx+1=sin²x
1-2sin²x-sinx+1=sin²x
3sin²x+sinx-2=0
sinx=b
3b²+b-2=0
D=1+24=25
b1=(-1-5)/6=-1⇒sinx=-1∉ОДЗ
a2=(-1+5)/6=2/3⇒sinx=2/3
x=arcsin2/3+2πn,n∈z∉[π/2;π]
x=π-arcsin2/3+2πn,n∈z
x=π-arcsin2/3∈[π/2;π]