let-give-x-lt-1-prove-that-n-1-sin-n-n-x-n-arctan-xsin-1-xcos-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 32937 by abdo imad last updated on 06/Apr/18

let give ∣x∣<1 prove that Σ_(n=1) ^∞ ((sin(nθ))/n) x^n =arctan( ((xsinθ)/(1−xcosθ))) .

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

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let-give-x-lt-1-prove-that-n-1-sin-n-n-x-n-arctan-xsin-1-xcos-

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