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Mathematics
Mathematics
Problem
Prove that
∑
k
=
1
100
sin
(
k
x
)
cos
(
(
101
−
k
)
x
)
=
50
sin
(
101
x
)
.
\sum_{k=1}^{100} \sin(kx)\cos\bigl((101-k)x\bigr)=50\sin(101x).
k
=
1
∑
100
sin
(
k
x
)
cos
(
(
101
−
k
)
x
)
=
50
sin
(
101
x
)
.
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