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Prove that: sum(k=1)^(100)sin(k x)cos(10...

Prove that: `sum_(k=1)^(100)sin(k x)cos(101-k)x=50"sin"(101 x)`

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Prove that: sum_(k=1)^(100)sin(kx)cos(101-k)x=50sin(101x)

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