Prove that _ k=1 ^ n-1 ^n C_k [ kx (n+k)x + (n-k)x (2n-k)x] = (2^n - 2) nx.

MATHEMATICS · Subjective · CBSE · Mathematics · Binomial Theorem · Binomial Theorem

Problem

Prove that ∑k=1n−1nCk[cos⁡kx⋅cos⁡(n+k)x+sin⁡(n−k)x⋅sin⁡(2n−k)x]=(2n−2)cos⁡nx.\sum_{k=1}^{n-1} {}^n C_k [\cos kx \cdot \cos(n+k)x + \sin(n-k)x \cdot \sin(2n-k)x] = (2^n - 2) \cos nx.

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