let-give-x-lt-1-prove-that-n-1-x-n-sin-n-x-sin-1-2x-cos-x-2-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 32935 by abdo imad last updated on 06/Apr/18

let give ∣x∣<1 prove that Σ_(n=1) ^∞ x^n sin(nθ) = ((x sinθ)/(1−2x cosθ +x^2 )) .

$${let}\:{give}\:\mid{x}\mid<\mathrm{1}\:\:{prove}\:{that} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:{x}^{{n}} {sin}\left({n}\theta\right)\:=\:\:\frac{{x}\:{sin}\theta}{\mathrm{1}−\mathrm{2}{x}\:{cos}\theta\:+{x}^{\mathrm{2}} }\:. \\ $$

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let-give-x-lt-1-prove-that-n-1-x-n-sin-n-x-sin-1-2x-cos-x-2-

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