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sin2α=2sinαcosα
sinα*cosβ=1/2(sin(α+β)+sin(α-β))
![4sin \alpha *cos \alpha *cos2 \alpha =2*2sin \alpha *cos \alpha*cos2 \alpha =2 *sin2 \alpha * cos2 \alpha = \\ =2* \frac{1}{2} (sin( 2 \alpha +2 \alpha )+sin( 2 \alpha -2 \alpha ))= 1*(sin4 \alpha +sin0)= \\ =1*(sin4 \alpha +0)=1*sin4 \alpha =sin4 \alpha 4sin \alpha *cos \alpha *cos2 \alpha =2*2sin \alpha *cos \alpha*cos2 \alpha =2 *sin2 \alpha * cos2 \alpha = \\ =2* \frac{1}{2} (sin( 2 \alpha +2 \alpha )+sin( 2 \alpha -2 \alpha ))= 1*(sin4 \alpha +sin0)= \\ =1*(sin4 \alpha +0)=1*sin4 \alpha =sin4 \alpha](https://tex.z-dn.net/?f=4sin+%5Calpha+%2Acos+%5Calpha+%2Acos2+%5Calpha+%3D2%2A2sin+%5Calpha+%2Acos+%5Calpha%2Acos2+%5Calpha+%3D2+%2Asin2+%5Calpha+%2A+cos2+%5Calpha+%3D+%5C%5C+%3D2%2A+%5Cfrac%7B1%7D%7B2%7D+%28sin%28+2+%5Calpha+%2B2+%5Calpha+%29%2Bsin%28+2+%5Calpha+-2+%5Calpha+%29%29%3D+1%2A%28sin4+%5Calpha+%2Bsin0%29%3D+%5C%5C+%3D1%2A%28sin4+%5Calpha+%2B0%29%3D1%2Asin4+%5Calpha+%3Dsin4+%5Calpha+)
sinα*cosβ=1/2(sin(α+β)+sin(α-β))
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