Докажи тождество: 1) {\sin \alpha \sin (\beta + \gamma) -\sin \beta \sin (\gamma + \alpha) \mathrlap{\:+}} {+\sin \gamma \sin (\alpha +\beta)=2\sin \alpha \cos \beta \sin \gamma }; 2) {\cos \alpha \cos (\beta + \gamma) -\cos \beta \cos (\gamma + \alpha) \mathrlap{\:+}} {+\cos \gamma \cos (\alpha -\beta)=\cos (\alpha -\beta -\gamma) }.

Задание

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Докажи тождество:

\({\sin \alpha \sin (\beta + \gamma) -\sin \beta \sin (\gamma + \alpha) \mathrlap{\:+}}\) \({+\sin \gamma \sin (\alpha +\beta)=2\sin \alpha \cos \beta \sin \gamma }\) ;
\({\cos \alpha \cos (\beta + \gamma) -\cos \beta \cos (\gamma + \alpha) \mathrlap{\:+}}\) \({+\cos \gamma \cos (\alpha -\beta)=\cos (\alpha -\beta -\gamma) }\) .