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Formule goniometriche

addizione, 2

Posto
	


quindi
	


allora
	sin(x+a) = Area(OAD)
Inoltre, poiché
	


	


	


quindi
	sinx·cosa=2Area(OKD)=2(Area(OLD)+Area(LKD))
	sina·cosx=2Area(OHA)=2(Area(OKA)-Area(HKA)).
Dato che Area(AKD)=Area(AKH), si ha infine
	Area(OAD)=sinx·cosa+sina·cosx
e quindi
	

sin(x+a)=sinx·cosa+sina·cosx


pagina di Roberto Ricci L.S. "A. Righi", Bologna. Ultima revisione