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Problem
Problem
The maximum value of
(
cos
α
1
)
(
cos
α
2
)
…
(
cos
α
n
)
(\cos \alpha_1)(\cos \alpha_2)\dots(\cos \alpha_n)
(
cos
α
1
)
(
cos
α
2
)
…
(
cos
α
n
)
under the restrictions
0
≤
α
1
,
α
2
,
…
,
α
n
≤
π
2
0 \le \alpha_1, \alpha_2, \dots, \alpha_n \le \frac{\pi}{2}
0
≤
α
1
,
α
2
,
…
,
α
n
≤
2
π
and
(
cot
α
1
)
(
cot
α
2
)
…
(
cot
α
n
)
=
1
(\cot \alpha_1)(\cot \alpha_2)\dots(\cot \alpha_n) = 1
(
cot
α
1
)
(
cot
α
2
)
…
(
cot
α
n
)
=
1
is a.
1
2
n
/
2
\frac{1}{2^{n/2}}
2
n
/2
1
b.
1
2
n
\frac{1}{2^n}
2
n
1
c.
1
2
n
\frac{1}{2n}
2
n
1
d. 1
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