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Формулы: ![\sin ( \alpha \pm \beta )=\sin \alpha \cos \beta \pm \sin \beta \cos \alpha \sin ( \alpha \pm \beta )=\sin \alpha \cos \beta \pm \sin \beta \cos \alpha](https://tex.z-dn.net/?f=%5Csin+%28+%5Calpha+%5Cpm+%5Cbeta+%29%3D%5Csin++%5Calpha+%5Ccos++%5Cbeta+%5Cpm+%5Csin++%5Cbeta+%5Ccos++%5Calpha+)
![\frac{\sin( \alpha + \beta )}{\sin( \alpha - \beta )} = \frac{\sin \alpha \cos \beta +\sin \beta \cos \alpha }{\sin \alpha \cos \beta -\sin \beta \cos \alpha } = \frac{\sin( \alpha + \beta )}{\sin( \alpha - \beta )} = \frac{\sin \alpha \cos \beta +\sin \beta \cos \alpha }{\sin \alpha \cos \beta -\sin \beta \cos \alpha } =](https://tex.z-dn.net/?f=+%5Cfrac%7B%5Csin%28+%5Calpha+%2B+%5Cbeta+%29%7D%7B%5Csin%28+%5Calpha+-+%5Cbeta+%29%7D+%3D+%5Cfrac%7B%5Csin++%5Calpha+%5Ccos++%5Cbeta+%2B%5Csin++%5Cbeta+%5Ccos++%5Calpha+%7D%7B%5Csin++%5Calpha+%5Ccos++%5Cbeta+-%5Csin++%5Cbeta+%5Ccos++%5Calpha+%7D+%3D)
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и ![\cos \beta \cos \beta](https://tex.z-dn.net/?f=%5Ccos++%5Cbeta+)
![=\dfrac{ \frac{\sin \alpha \cos \beta }{\cos \alpha \cos \beta } + \frac{\sin \alpha \cos \beta }{\cos \alpha \cos \beta } }{ \frac{\sin \alpha \cos \beta }{\cos \alpha \cos \beta }- \frac{\sin \beta \cos \alpha }{\cos \alpha \cos \beta } } = \dfrac{ \frac{\sin \alpha }{\cos \alpha }+ \frac{\sin \beta }{\cos \beta } }{ \frac{\sin \alpha }{\cos \alpha }- \frac{\sin \beta }{\cos \beta } } = \frac{tg \alpha +tg \beta }{tg \alpha -tg \beta } =\dfrac{ \frac{\sin \alpha \cos \beta }{\cos \alpha \cos \beta } + \frac{\sin \alpha \cos \beta }{\cos \alpha \cos \beta } }{ \frac{\sin \alpha \cos \beta }{\cos \alpha \cos \beta }- \frac{\sin \beta \cos \alpha }{\cos \alpha \cos \beta } } = \dfrac{ \frac{\sin \alpha }{\cos \alpha }+ \frac{\sin \beta }{\cos \beta } }{ \frac{\sin \alpha }{\cos \alpha }- \frac{\sin \beta }{\cos \beta } } = \frac{tg \alpha +tg \beta }{tg \alpha -tg \beta }](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B+%5Cfrac%7B%5Csin++%5Calpha+%5Ccos++%5Cbeta+%7D%7B%5Ccos++%5Calpha+%5Ccos++%5Cbeta+%7D+%2B+%5Cfrac%7B%5Csin++%5Calpha+%5Ccos++%5Cbeta+%7D%7B%5Ccos+%5Calpha+%5Ccos++%5Cbeta+%7D+%7D%7B+%5Cfrac%7B%5Csin++%5Calpha+%5Ccos+%5Cbeta+%7D%7B%5Ccos++%5Calpha+%5Ccos++%5Cbeta+%7D-+%5Cfrac%7B%5Csin++%5Cbeta+%5Ccos++%5Calpha+%7D%7B%5Ccos++%5Calpha+%5Ccos++%5Cbeta+%7D++%7D+%3D+%5Cdfrac%7B+%5Cfrac%7B%5Csin++%5Calpha+%7D%7B%5Ccos++%5Calpha+%7D%2B+%5Cfrac%7B%5Csin+%5Cbeta+%7D%7B%5Ccos++%5Cbeta+%7D++%7D%7B+%5Cfrac%7B%5Csin++%5Calpha+%7D%7B%5Ccos++%5Calpha+%7D-+%5Cfrac%7B%5Csin+%5Cbeta+%7D%7B%5Ccos++%5Cbeta+%7D++%7D+%3D+%5Cfrac%7Btg+%5Calpha+%2Btg+%5Cbeta+%7D%7Btg+%5Calpha+-tg+%5Cbeta+%7D+)
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