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KEAM 2019 Math Paper
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© examsnet.com
Question : 88
Total: 121
The value of
cos
‌
2
Ï€
7
+
cos
‌
4
Ï€
7
+
cos
‌
6
Ï€
7
is equal to
−
1
1
‌
−
1
2
‌
1
2
0
Validate
Solution:
cos
(
‌
2
Ï€
7
)
+
cos
(
‌
4
Ï€
7
)
+
cos
(
‌
6
Ï€
7
)
=
R
e
{
e
‌
2
Ï€
i
7
+
e
‌
4
Ï€
i
7
+
e
‌
6
Ï€
i
7
}
‌
‌
[
e
2
Ï€
i
∕
7
+
e
4
Ï€
i
∕
7
+
e
6
Ï€
i
∕
7
+
e
−
2
Ï€
i
∕
7
=
‌
+
e
−
4
Ï€
i
∕
7
+
e
−
6
Ï€
i
∕
7
]
2
=
‌
−
1
+
(
‌
sum of seven roots of unity
‌
)
2
=
‌
1
+
0
2
=
‌
−
1
2
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