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Problem
Problem
If
k
sin
2
x
+
1
k
csc
2
x
=
2
,
x
∈
(
0
,
π
2
)
k \sin^2 x + \frac{1}{k} \csc^2 x = 2, x \in \left(0, \frac{\pi}{2}\right)
k
sin
2
x
+
k
1
csc
2
x
=
2
,
x
∈
(
0
,
2
π
)
, then
cos
2
x
+
5
sin
x
cos
x
+
6
sin
2
x
\cos^2 x + 5 \sin x \cos x + 6 \sin^2 x
cos
2
x
+
5
sin
x
cos
x
+
6
sin
2
x
is equal to a.
k
2
+
5
k
+
6
k
2
\frac{k^2 + 5k + 6}{k^2}
k
2
k
2
+
5
k
+
6
b.
k
2
−
5
k
+
6
k
2
\frac{k^2 - 5k + 6}{k^2}
k
2
k
2
−
5
k
+
6
c. 6 d. None of these
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