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Byju's Answer
Standard XII
Mathematics
Transforming Product of Trigonometric Functions into Sum or Difference
The maximum v...
Question
The maximum value of
cos
α
1
.
cos
α
2
.
.
.
.
.
.
cos
α
n
∀
0
≤
α
1
,
α
2
,
⋯
,
α
n
≤
π
2
&
cot
α
1
.
cot
α
2
.
.
.
.
.
.
cot
α
n
=
1
is:
Open in App
Solution
Given
(
cot
α
1
)
.
(
cot
α
2
)
.
.
.
.
.
(
cot
α
n
)
=
1
∴
cos
α
1
.
cos
α
2
.
.
.
cos
α
n
=
sin
α
1
.
sin
α
2
.
.
.
sin
α
n
Now,
(
cos
α
1
.
cos
α
2
.
.
.
cos
α
n
)
2
=
(
cos
α
1
.
cos
α
2
.
.
.
cos
α
n
)
.
(
cos
α
1
.
cos
α
2
.
.
.
cos
α
n
)
=
(
cos
α
1
.
cos
α
2
.
.
.
cos
α
n
)
.
(
sin
α
1
.
sin
α
2
.
.
.
sin
α
n
)
=
1
2
n
sin
2
α
1
.
sin
2
α
2
.
.
.
sin
2
α
n
.
∵
0
≤
α
1
,
α
2
,
.
.
.
.
.
,
α
n
≤
π
2
∴
0
≤
2
α
1
,
2
α
2
,
.
.
.
.
.
,
2
α
n
≤
π
So each of
sin
2
α
1
≤
1
∴
(
cos
α
1
.
cos
α
2
.
.
.
cos
α
n
)
2
≤
1
2
n
.
But each of
cos
α
1
is positive.
∴
cos
α
1
.
cos
α
2
.
.
.
.
cos
α
n
≤
√
1
2
n
⇒
cos
α
1
.
cos
α
2
.
.
.
.
cos
α
n
≤
1
2
n
2
.
So the maximum value of
cos
α
1
.
cos
α
2
.
.
.
.
.
.
cos
α
n
=
1
2
n
2
Hence the correct answer is Option A.
Suggest Corrections
0
Similar questions
Q.
The maximum value of
(
cos
α
1
)
⋅
(
cos
α
2
)
⋯
(
cos
α
n
)
. Under the restrictions
0
≤
α
1
,
α
2
,
…
α
n
≤
π
2
,
(
cot
α
1
)
⋅
(
cot
α
2
)
⋯
(
cot
α
n
)
=
1
is
Q.
The maximum values of
cos
α
1
⋅
cos
α
2
⋅
.
.
.
⋅
cos
α
n
, under the restrictions
0
≤
α
1
,
α
2
,
.
.
.
,
α
n
≤
π
2
and
cot
α
1
⋅
cot
α
2
⋅
.
.
.
cot
α
n
=
1
, is
Q.
The maximum value of
(
cos
α
1
)
.
(
cos
α
2
)
.
.
.
.
.
.
.
(
cos
α
n
)
, under the restriction
0
≤
α
1
,
α
2
,
.
.
.
.
.
.
,
α
n
≤
π
2
and
cot
α
1
.
cot
α
2
.
.
.
.
.
.
.
cot
α
n
=
1
is:
Q.
The maximum value of
cos
α
1
⋅
cos
α
2
⋅
cos
α
3
⋯
cos
α
n
under the restriction
0
≤
α
1
,
α
2
,
…
,
α
n
≤
π
2
and
cot
α
1
⋅
cot
α
2
⋯
cot
α
n
=
1
is
Q.
If
0
<
α
1
<
α
2
<
…
…
<
α
n
<
π
2
, then
t
a
n
α
1
<
s
i
n
α
1
+
s
i
n
α
2
+
…
…
+
s
i
n
α
n
c
o
s
α
1
+
c
o
s
α
2
+
…
…
+
α
n
<
t
a
n
α
n
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