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On the correctness of the determination of trigonometric functions by the system of functional equations

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Author(s): Е. V. Velichko | I. G. Tkachenko

Journal: Carpathian Mathematical Publications
ISSN 2075-9827

Volume: 3;
Issue: 1;
Start page: 15;
Date: 2011;
Original page

ABSTRACT
The article shows that the system of the functional equations$S(x+y)=S(x)C(y)+S(y)C(x),,C(x+y)=C(x)C(y)-S(y)S(x)$ defines abroader class of the functions than the trigonometric equations. Theconditions, which must be added to this system to obtain the uniquesolution have been developed $S(x)=sin{ax},,C(x)=cos{ax}$. Themethod of the reduction of the functional equations to thedifferential equations is used.
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