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3. ![tg2 alpha=frac{sin2alpha}{cos2alpha} \ \
sin alpha =- sqrt{1-cos^2 alpha } =- sqrt{1- frac{5}{9} }=- frac{2}{3} \ \
sin2 alpha =2sin alpha*cos alpha = frac{2*2* sqrt{5} }{3*3}=frac{4 sqrt{5} }{9} \ \
cos2 alpha =cos^2 alpha -sin ^2 alpha =frac{5}{9}-frac{4}{9}=frac{1}{9} \ \
tg2 alpha = frac{4 sqrt{5} }{9}: frac{1}{9}=4sqrt{5} \ \](https://tex.z-dn.net/?f=tg2+alpha%3Dfrac%7Bsin2alpha%7D%7Bcos2alpha%7D++%5C++%5C+%0Asin+alpha+%3D-+sqrt%7B1-cos%5E2+alpha+%7D+%3D-+sqrt%7B1-+frac%7B5%7D%7B9%7D+%7D%3D-+frac%7B2%7D%7B3%7D+%5C++%5C+%0Asin2+alpha+%3D2sin+alpha%2Acos+alpha+%3D+frac%7B2%2A2%2A+sqrt%7B5%7D+%7D%7B3%2A3%7D%3Dfrac%7B4+sqrt%7B5%7D+%7D%7B9%7D+%5C++%5C+%0Acos2+alpha+%3Dcos%5E2+alpha+-sin+%5E2+alpha+%3Dfrac%7B5%7D%7B9%7D-frac%7B4%7D%7B9%7D%3Dfrac%7B1%7D%7B9%7D+%5C++%5C+%0Atg2+alpha+%3D+frac%7B4+sqrt%7B5%7D+%7D%7B9%7D%3A+frac%7B1%7D%7B9%7D%3D4sqrt%7B5%7D+%5C++%5C+ "tg2 alpha=frac{sin2alpha}{cos2alpha} \ \
sin alpha =- sqrt{1-cos^2 alpha } =- sqrt{1- frac{5}{9} }=- frac{2}{3} \ \
sin2 alpha =2sin alpha*cos alpha = frac{2*2* sqrt{5} }{3*3}=frac{4 sqrt{5} }{9} \ \
cos2 alpha =cos^2 alpha -sin ^2 alpha =frac{5}{9}-frac{4}{9}=frac{1}{9} \ \
tg2 alpha = frac{4 sqrt{5} }{9}: frac{1}{9}=4sqrt{5} \ \")
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