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Question
Mathematics
The value of cos (π/15) cos (2π/15) cos (4π/15) cos (8π/15) is
Q. The value of
cos
15
π
cos
15
2
π
cos
15
4
π
cos
15
8
π
is
1934
209
WBJEE
WBJEE 2008
Trigonometric Functions
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A
16
1
38%
B
−
16
1
29%
C
1
18%
D
0
15%
Solution:
cos
15
π
⋅
cos
15
2
π
⋅
cos
15
4
π
⋅
cos
15
8
π
=
4
1
(
2
cos
15
4
π
cos
15
π
)
(
2
cos
15
8
π
cos
15
2
π
)
=
4
1
(
cos
6
0
∘
+
cos
3
6
∘
)
(
cos
12
0
∘
+
cos
7
2
∘
)
=
4
1
(
2
1
+
4
5
+
1
)
(
−
2
1
+
4
5
−
1
)
(
∵
cos
3
6
∘
=
4
5
+
1
and
cos
7
2
∘
=
4
5
−
1
)
=
4
1
[
−
4
1
+
2
1
(
4
5
−
1
−
4
5
+
1
)
+
16
5
−
1
]
=
4
1
[
2
1
(
−
2
1
)
]
=
−
16
1