If 2 sin theta + cosec theta = 3, then find the value of sin^4 theta + 1/sin^2 theta.
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2sin@+cosec@=3,
2sin@ + 1/sin@ =3,
2sin²@-3sin@+1=0
2sin²@-(2+1)sin@+1=0,
2sin²@-2sin@-sin@+1=0,
2sin@(sin@-1)-1(sin@-1)=0,
(sin@-1)(2sin@-1)=0,
if
sin@-1=0,
sin@=1,
@=90°,
and if
2sin@-1=0,
sin@=1/2,
@=30°,
so
sin⁴@+1/sin²@ ,
(sin90°)⁴+1/(sin90°)²,
1+1=2,
same put @=30°
2sin@ + 1/sin@ =3,
2sin²@-3sin@+1=0
2sin²@-(2+1)sin@+1=0,
2sin²@-2sin@-sin@+1=0,
2sin@(sin@-1)-1(sin@-1)=0,
(sin@-1)(2sin@-1)=0,
if
sin@-1=0,
sin@=1,
@=90°,
and if
2sin@-1=0,
sin@=1/2,
@=30°,
so
sin⁴@+1/sin²@ ,
(sin90°)⁴+1/(sin90°)²,
1+1=2,
same put @=30°
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