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а)![sin alpha = frac{ sqrt{3} }{5}, cos alpha = frac{ sqrt{22} }{5};
cos^{2} alpha + sin^{2} alpha =1, frac{3}{25}+ frac{22}{25}=1;
sin alpha = frac{ sqrt{3} }{5}, cos alpha = frac{ sqrt{22} }{5};
cos^{2} alpha + sin^{2} alpha =1, frac{3}{25}+ frac{22}{25}=1;](https://tex.z-dn.net/?f=sin+alpha+%3D+frac%7B+sqrt%7B3%7D+%7D%7B5%7D%2C+cos+alpha+%3D+frac%7B+sqrt%7B22%7D+%7D%7B5%7D%3B%0A+cos%5E%7B2%7D+alpha+%2B+sin%5E%7B2%7D+alpha+%3D1%2C++frac%7B3%7D%7B25%7D%2B+frac%7B22%7D%7B25%7D%3D1%3B++++%0A++)
Можуть!
б)![tg alpha = sqrt{3}+1, ctg alpha = sqrt{3}-1;
ctg alpha = frac{1}{tg alpha } = frac{1}{ sqrt{3}+1 }= frac{ sqrt{3}-1 }{ (sqrt{3} -1)( sqrt{3} +1)}= tg alpha = sqrt{3}+1, ctg alpha = sqrt{3}-1;
ctg alpha = frac{1}{tg alpha } = frac{1}{ sqrt{3}+1 }= frac{ sqrt{3}-1 }{ (sqrt{3} -1)( sqrt{3} +1)}=](https://tex.z-dn.net/?f=tg+alpha+%3D+sqrt%7B3%7D%2B1%2C+ctg+alpha+%3D+sqrt%7B3%7D-1%3B%0Actg+alpha+%3D+frac%7B1%7D%7Btg+alpha+%7D+%3D+frac%7B1%7D%7B+sqrt%7B3%7D%2B1+%7D%3D+frac%7B+sqrt%7B3%7D-1+%7D%7B+%28sqrt%7B3%7D+-1%29%28+sqrt%7B3%7D+%2B1%29%7D%3D++++++)
![frac{ sqrt{3}-1 }{2} neq sqrt{3}-1; ctg alpha neq frac{1}{tg alpha } ; frac{ sqrt{3}-1 }{2} neq sqrt{3}-1; ctg alpha neq frac{1}{tg alpha } ;](https://tex.z-dn.net/?f=+frac%7B+sqrt%7B3%7D-1+%7D%7B2%7D++neq++sqrt%7B3%7D-1%3B+ctg+alpha++neq++frac%7B1%7D%7Btg+alpha+%7D+%3B+)
Не можуть!
Можуть!
б)
Не можуть!
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