Prove that _ k=1 ^ 100 (kx) ((101-k)x )=50 (101x).

MATHEMATICS · Subjective · ISC · Mathematics · Sets and Functions · Sets and Functions

Problem

Prove that ∑k=1100sin⁡(kx)cos⁡((101−k)x)=50sin⁡(101x).\sum_{k=1}^{100} \sin(kx)\cos\bigl((101-k)x\bigr)=50\sin(101x).

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