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Problem
Problem
Assertion (Statement I): In a
Δ
A
B
C
\Delta ABC
Δ
A
B
C
, if
cos
2
A
2
+
cos
2
B
2
+
cos
2
C
2
=
y
(
x
2
+
1
x
2
)
\cos^2 \frac{A}{2} + \cos^2 \frac{B}{2} + \cos^2 \frac{C}{2} = y \left( x^2 + \frac{1}{x^2} \right)
cos
2
2
A
+
cos
2
2
B
+
cos
2
2
C
=
y
(
x
2
+
x
2
1
)
, then the maximum value of
y
y
y
is
9
8
\frac{9}{8}
8
9
. Reason (Statement II): In a
Δ
A
B
C
\Delta ABC
Δ
A
B
C
,
sin
A
2
⋅
sin
B
2
⋅
sin
C
2
≤
1
8
\sin \frac{A}{2} \cdot \sin \frac{B}{2} \cdot \sin \frac{C}{2} \le \frac{1}{8}
sin
2
A
⋅
sin
2
B
⋅
sin
2
C
≤
8
1
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