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Mathematics
Mathematics
Problem
The value of
∑
k
=
1
13
1
sin
(
π
4
+
(
k
−
1
)
π
6
)
sin
(
π
4
+
k
π
6
)
\sum_{k=1}^{13} \frac{1}{\sin \left( \frac{\pi}{4} + \frac{(k-1)\pi}{6} \right) \sin \left( \frac{\pi}{4} + \frac{k\pi}{6} \right)}
∑
k
=
1
13
s
i
n
(
4
π
+
6
(
k
−
1
)
π
)
s
i
n
(
4
π
+
6
k
π
)
1
is equal to a.
3
−
3
3 - \sqrt{3}
3
−
3
b.
2
(
3
−
3
)
2(3 - \sqrt{3})
2
(
3
−
3
)
c.
2
(
3
−
1
)
2(\sqrt{3} - 1)
2
(
3
−
1
)
d.
2
(
2
+
3
)
2(2 + \sqrt{3})
2
(
2
+
3
)
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