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1) косинус двойного угла
![1-2sin^2(5alpha)=cos(2*5alpha)=cos(10alpha) 1-2sin^2(5alpha)=cos(2*5alpha)=cos(10alpha)](https://tex.z-dn.net/?f=1-2sin%5E2%285alpha%29%3Dcos%282%2A5alpha%29%3Dcos%2810alpha%29)
2) тоже косинус двойного угла
![2cos^2(3alpha)-1=cos(2*3alpha)=cos(6alpha) 2cos^2(3alpha)-1=cos(2*3alpha)=cos(6alpha)](https://tex.z-dn.net/?f=2cos%5E2%283alpha%29-1%3Dcos%282%2A3alpha%29%3Dcos%286alpha%29)
формула косинуса двойного угла:
![cos(2x)=cos^2x-sin^2x=1-2sin^2x=2cos^2x-1 cos(2x)=cos^2x-sin^2x=1-2sin^2x=2cos^2x-1](https://tex.z-dn.net/?f=cos%282x%29%3Dcos%5E2x-sin%5E2x%3D1-2sin%5E2x%3D2cos%5E2x-1)
3) формула произведения синуса на косинус
![sina*cosb= frac{sin(a-b)+sin(a+b)}{2} sina*cosb= frac{sin(a-b)+sin(a+b)}{2}](https://tex.z-dn.net/?f=sina%2Acosb%3D+frac%7Bsin%28a-b%29%2Bsin%28a%2Bb%29%7D%7B2%7D+)
![frac{1-cos2alpha}{ frac{sin( frac{alpha}{2}-frac{alpha}{2})+sin(frac{alpha}{2}+frac{alpha}{2}) }{2} } = frac{1-cos2alpha}{ frac{sinalpha}{2} } = frac{1-(1-2sin^2alpha)}{frac{sinalpha}{2}} = 2*2*sinalpha=4sinalpha frac{1-cos2alpha}{ frac{sin( frac{alpha}{2}-frac{alpha}{2})+sin(frac{alpha}{2}+frac{alpha}{2}) }{2} } = frac{1-cos2alpha}{ frac{sinalpha}{2} } = frac{1-(1-2sin^2alpha)}{frac{sinalpha}{2}} = 2*2*sinalpha=4sinalpha](https://tex.z-dn.net/?f=+frac%7B1-cos2alpha%7D%7B+frac%7Bsin%28+frac%7Balpha%7D%7B2%7D-frac%7Balpha%7D%7B2%7D%29%2Bsin%28frac%7Balpha%7D%7B2%7D%2Bfrac%7Balpha%7D%7B2%7D%29+%7D%7B2%7D+%7D+%3D+frac%7B1-cos2alpha%7D%7B+frac%7Bsinalpha%7D%7B2%7D+%7D+%3D+frac%7B1-%281-2sin%5E2alpha%29%7D%7Bfrac%7Bsinalpha%7D%7B2%7D%7D+%3D+2%2A2%2Asinalpha%3D4sinalpha)
4)формула косинуса половинного аргумента
![cos^2( frac{alpha}{2} )= frac{1+cosalpha}{2} cos^2( frac{alpha}{2} )= frac{1+cosalpha}{2}](https://tex.z-dn.net/?f=cos%5E2%28+frac%7Balpha%7D%7B2%7D+%29%3D+frac%7B1%2Bcosalpha%7D%7B2%7D+)
![frac{2*frac{1+cosalpha}{2}-1}{2sinalpha*cosalpha} = frac{cosalpha}{2sinalpha*cosalpha} = frac{1}{2sinalpha} frac{2*frac{1+cosalpha}{2}-1}{2sinalpha*cosalpha} = frac{cosalpha}{2sinalpha*cosalpha} = frac{1}{2sinalpha}](https://tex.z-dn.net/?f=+frac%7B2%2Afrac%7B1%2Bcosalpha%7D%7B2%7D-1%7D%7B2sinalpha%2Acosalpha%7D+%3D+frac%7Bcosalpha%7D%7B2sinalpha%2Acosalpha%7D+%3D+frac%7B1%7D%7B2sinalpha%7D+)
5)
![1+cos4alpha=1+cos(2*2alpha)=1+cos^2(2alpha)-sin^2(2alpha)=cos^2(2alpha)+\(1-sin^2(2alpha))=cos^2(2alpha)+cos^2(2alpha)=2cos^2(2alpha) 1+cos4alpha=1+cos(2*2alpha)=1+cos^2(2alpha)-sin^2(2alpha)=cos^2(2alpha)+\(1-sin^2(2alpha))=cos^2(2alpha)+cos^2(2alpha)=2cos^2(2alpha)](https://tex.z-dn.net/?f=1%2Bcos4alpha%3D1%2Bcos%282%2A2alpha%29%3D1%2Bcos%5E2%282alpha%29-sin%5E2%282alpha%29%3Dcos%5E2%282alpha%29%2B%5C%281-sin%5E2%282alpha%29%29%3Dcos%5E2%282alpha%29%2Bcos%5E2%282alpha%29%3D2cos%5E2%282alpha%29)
6)
![1-2cos^2(5alpha)=-(2cos^2(5alpha)-1)=-cos(2*5alpha)=-cos(10alpha) 1-2cos^2(5alpha)=-(2cos^2(5alpha)-1)=-cos(2*5alpha)=-cos(10alpha)](https://tex.z-dn.net/?f=1-2cos%5E2%285alpha%29%3D-%282cos%5E2%285alpha%29-1%29%3D-cos%282%2A5alpha%29%3D-cos%2810alpha%29)
2) тоже косинус двойного угла
формула косинуса двойного угла:
3) формула произведения синуса на косинус
4)формула косинуса половинного аргумента
5)
6)
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