Součin goniometrických funkcí

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sinx, cosx

  • \sin \alpha \sin \beta = \frac{1}{2} \left [ \cos(\alpha - \beta ) - \cos(\alpha + \beta )\right ]


  • \cos \alpha \cos \beta = \frac{1}{2} \left [ \cos(\alpha - \beta ) + \cos(\alpha + \beta )\right ]


  • \sin \alpha \cos \beta = \frac{1}{2} \left [ \sin(\alpha + \beta ) + \sin(\alpha - \beta )\right ]


  • \cos \alpha \sin \beta = \frac{1}{2} \left [ \sin(\alpha + \beta ) - \sin(\alpha - \beta )\right ]

tgx, cotgx

  • \operatorname{tg} \alpha \; \operatorname{tg} \beta = \frac{\operatorname{tg} \alpha + \operatorname{tg} \beta}{\operatorname{cotg} \alpha + \operatorname{cotg} \beta} = -\frac{\operatorname{tg} \alpha - \operatorname{tg} \beta}{\operatorname{cotg} \alpha - \operatorname{cotg} \beta}


  • \operatorname{cotg} \alpha \;\operatorname{cotg} \beta = \frac{\operatorname{cotg} \alpha + \operatorname{cotg} \beta}{\operatorname{tg} \alpha + \operatorname{tg} \beta} = -\frac{\operatorname{cotg} \alpha - \operatorname{cotg} \beta}{\operatorname{tg} \alpha - \operatorname{tg} \beta}


  • \operatorname{tg} \alpha \;\operatorname{cotg} \beta = \frac{\operatorname{tg} \alpha + \operatorname{cotg} \beta}{\operatorname{cotg} \alpha + \operatorname{tg} \beta} = -\frac{\operatorname{tg} \alpha - \operatorname{cotg} \beta}{\operatorname{cotg} \alpha - \operatorname{tg} \beta}


  • \operatorname{cotg} \alpha \;\operatorname{tg} \beta = \frac{\operatorname{cotg} \alpha + \operatorname{tg} \beta}{\operatorname{tg} \alpha + \operatorname{cotg} \beta} = -\frac{\operatorname{cotg} \alpha - \operatorname{tg} \beta}{\operatorname{tg} \alpha - \operatorname{cotg} \beta}

Zdroj

Bartsch, H.-J.:Matematické vzorce, ISBN 80-204-0607-7

Citováno z „http://panwiki.panska.cz/index.php/Sou%C4%8Din_goniometrick%C3%BDch_funkc%C3%AD“