Предмет: Алгебра,
автор: раб1
Решите пожалуйста 1,3,4, задания, по желанию можете решить 2
Приложения:
![](https://files.topotvet.com/i/a4c/a4c836fabae1c3059417200abc2b16b1.jpg)
Ответы
Автор ответа:
0
№1
![frac{tg alpha }{1 - tg^{2} alpha} * frac{ctg^{2} alpha - 1}{ctg alpha} = frac{tg alpha * tg alpha * (ctg^{2} alpha -1) }{1-tg^{2} alpha} = frac{tg^{2} alpha * (ctg^{2} alpha -1) }{1 - tg ^{2} alpha } = frac{1 - tg^{2} alpha }{1 - tg^{2} alpha } = 1 frac{tg alpha }{1 - tg^{2} alpha} * frac{ctg^{2} alpha - 1}{ctg alpha} = frac{tg alpha * tg alpha * (ctg^{2} alpha -1) }{1-tg^{2} alpha} = frac{tg^{2} alpha * (ctg^{2} alpha -1) }{1 - tg ^{2} alpha } = frac{1 - tg^{2} alpha }{1 - tg^{2} alpha } = 1](https://tex.z-dn.net/?f=frac%7Btg+alpha+%7D%7B1+-+tg%5E%7B2%7D+alpha%7D+%2A++frac%7Bctg%5E%7B2%7D+alpha+-+1%7D%7Bctg+alpha%7D+%3D++frac%7Btg+alpha+%2A+tg+alpha++%2A+%28ctg%5E%7B2%7D+alpha+-1%29+%7D%7B1-tg%5E%7B2%7D+alpha%7D+%3D++frac%7Btg%5E%7B2%7D+alpha+%2A+%28ctg%5E%7B2%7D+alpha+-1%29+%7D%7B1+-+tg+%5E%7B2%7D+alpha++%7D+%3D++frac%7B1+-+tg%5E%7B2%7D+alpha++%7D%7B1+-+tg%5E%7B2%7D+alpha++%7D+%3D+1)
№2 - А
![frac{sin( frac{pi}{4} + alpha ) - cos( frac{pi}{4} + alpha ) }{sin( frac{pi}{4} + alpha ) + cos( frac{pi}{4} + alpha ) } = frac{sinfrac{ pi }{4} * cos alpha + cosfrac{ pi }{4} * sin alpha - cosfrac{ pi }{4} * cos alpha + sin frac{ pi }{4} * sin alpha }{sinfrac{ pi }{4} * cos alpha + cosfrac{ pi }{4} * sin alpha + cosfrac{ pi }{4} * cos alpha - sin frac{ pi }{4} * sin alpha } = frac{sin( frac{pi}{4} + alpha ) - cos( frac{pi}{4} + alpha ) }{sin( frac{pi}{4} + alpha ) + cos( frac{pi}{4} + alpha ) } = frac{sinfrac{ pi }{4} * cos alpha + cosfrac{ pi }{4} * sin alpha - cosfrac{ pi }{4} * cos alpha + sin frac{ pi }{4} * sin alpha }{sinfrac{ pi }{4} * cos alpha + cosfrac{ pi }{4} * sin alpha + cosfrac{ pi }{4} * cos alpha - sin frac{ pi }{4} * sin alpha } =](https://tex.z-dn.net/?f=frac%7Bsin%28+frac%7Bpi%7D%7B4%7D+%2B++alpha+%29+-+cos%28+frac%7Bpi%7D%7B4%7D+%2B++alpha+%29+%7D%7Bsin%28+frac%7Bpi%7D%7B4%7D+%2B++alpha+%29+%2B+cos%28+frac%7Bpi%7D%7B4%7D+%2B++alpha+%29+%7D++%3D++frac%7Bsinfrac%7B+pi+%7D%7B4%7D+%2A+cos+alpha+%2B+cosfrac%7B+pi+%7D%7B4%7D+%2A+sin+alpha+-+cosfrac%7B+pi+%7D%7B4%7D+%2A+cos+alpha++%2B+sin+frac%7B+pi+%7D%7B4%7D+%2A+sin+alpha++%7D%7Bsinfrac%7B+pi+%7D%7B4%7D+%2A+cos+alpha+%2B+cosfrac%7B+pi+%7D%7B4%7D+%2A+sin+alpha+%2B+cosfrac%7B+pi+%7D%7B4%7D+%2A+cos+alpha++-+sin+frac%7B+pi+%7D%7B4%7D+%2A+sin+alpha+%7D+%3D+)
![frac{ frac{ sqrt{2} }{2} * cos alpha + frac{ sqrt{2} }{2} * sin alpha - frac{ sqrt{2} }{2} * cos alpha + frac{ sqrt{2} }{2} * sin alpha }{ frac{ sqrt{2} }{2} * cos alpha + frac{ sqrt{2} }{2} * sin alpha + frac{ sqrt{2} }{2} * cos alpha - frac{ sqrt{2} }{2} * sin alpha} = frac{ frac{ sqrt{2} }{2} * sin alpha + frac{ sqrt{2} }{2} * sin alpha }{ frac{ sqrt{2} }{2} * cos alpha + frac{ sqrt{2} }{2}* cos alpha } =tgalpha frac{ frac{ sqrt{2} }{2} * cos alpha + frac{ sqrt{2} }{2} * sin alpha - frac{ sqrt{2} }{2} * cos alpha + frac{ sqrt{2} }{2} * sin alpha }{ frac{ sqrt{2} }{2} * cos alpha + frac{ sqrt{2} }{2} * sin alpha + frac{ sqrt{2} }{2} * cos alpha - frac{ sqrt{2} }{2} * sin alpha} = frac{ frac{ sqrt{2} }{2} * sin alpha + frac{ sqrt{2} }{2} * sin alpha }{ frac{ sqrt{2} }{2} * cos alpha + frac{ sqrt{2} }{2}* cos alpha } =tgalpha](https://tex.z-dn.net/?f=+frac%7B+frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%2A+cos+alpha+%2B+frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%2A+sin++alpha+-++frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%2A+cos+alpha+%2B++frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%2A+sin+alpha+++%7D%7B+frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%2A+cos+alpha+%2B+frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%2A+sin++alpha+%2B+frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%2A+cos+alpha+-++frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%2A+sin+alpha%7D++%3D++frac%7B+frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%2A+sin+alpha+%2B++frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%2A+sin+alpha++%7D%7B+frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%2A+cos++alpha++%2B++frac%7B+sqrt%7B2%7D+%7D%7B2%7D%2A+cos+alpha++%7D+%3Dtgalpha+)
№2 - Б
![frac{1 - cos( frac{3 pi }{2} - beta ) + cos (6 pi - beta )}{1+sin( beta + 8 pi ) - sin ( frac{3 pi }{2} + beta )} = frac{1 + sin beta + cos beta }{1 + sin beta + cos beta } = 1 frac{1 - cos( frac{3 pi }{2} - beta ) + cos (6 pi - beta )}{1+sin( beta + 8 pi ) - sin ( frac{3 pi }{2} + beta )} = frac{1 + sin beta + cos beta }{1 + sin beta + cos beta } = 1](https://tex.z-dn.net/?f=frac%7B1+-+cos%28+frac%7B3+pi+%7D%7B2%7D+-++beta+%29+%2B+cos+%286+pi++-++beta+%29%7D%7B1%2Bsin%28+beta+%2B+8+pi+%29+-+sin+%28+frac%7B3+pi+%7D%7B2%7D+%2B++beta+%29%7D+%3D++frac%7B1+%2B+sin+beta+%2B+cos+beta+%7D%7B1+%2B+sin+beta+%2B+cos+beta+%7D+%3D+1)
№3
![sin^{3} (- frac{9 pi }{4} ) + cos^{2} (- frac{5 pi }{2}) = ( - frac{ sqrt{2} }{2} )^{3} + 0 =
- frac{( sqrt{2})^{3} }{8} = - frac{ sqrt{2} }{4} sin^{3} (- frac{9 pi }{4} ) + cos^{2} (- frac{5 pi }{2}) = ( - frac{ sqrt{2} }{2} )^{3} + 0 =
- frac{( sqrt{2})^{3} }{8} = - frac{ sqrt{2} }{4}](https://tex.z-dn.net/?f=sin%5E%7B3%7D+%28-+frac%7B9+pi+%7D%7B4%7D+%29+%2B+cos%5E%7B2%7D+%28-+frac%7B5+pi+%7D%7B2%7D%29+%3D+%28+-+frac%7B+sqrt%7B2%7D+%7D%7B2%7D+%29%5E%7B3%7D++%2B+0+%3D%0A+-+frac%7B%28+sqrt%7B2%7D%29%5E%7B3%7D++%7D%7B8%7D+%3D+-+frac%7B+sqrt%7B2%7D+%7D%7B4%7D+)
№4
![cos( frac{7 pi }{2} + alpha) * tg( frac{ pi }{2} - alpha )- sin( frac{ pi }{2} - alpha ) + ctg ( frac{3 pi }{2} - alpha ) = tg alpha
\ sin alpha * ctg alpha - cos alpha +tg alpha = tg alpha
\ sin alpha * frac{cos alpha }{sin alpha } - cos alpha + tg alpha = tg alpha
\ cos alpha - cos alpha + tg alpha = tg alpha
cos( frac{7 pi }{2} + alpha) * tg( frac{ pi }{2} - alpha )- sin( frac{ pi }{2} - alpha ) + ctg ( frac{3 pi }{2} - alpha ) = tg alpha
\ sin alpha * ctg alpha - cos alpha +tg alpha = tg alpha
\ sin alpha * frac{cos alpha }{sin alpha } - cos alpha + tg alpha = tg alpha
\ cos alpha - cos alpha + tg alpha = tg alpha](https://tex.z-dn.net/?f=cos%28+frac%7B7+pi+%7D%7B2%7D+%2B++alpha%29+%2A+tg%28+frac%7B+pi+%7D%7B2%7D+-++alpha+%29-+sin%28+frac%7B+pi+%7D%7B2%7D+-++alpha+%29+%2B+ctg+%28+frac%7B3+pi+%7D%7B2%7D+-++alpha+%29+%3D+tg+alpha+%0A+%5C+sin++alpha++%2A+ctg+alpha++-+cos+alpha+%2Btg+alpha+%3D+tg+alpha+%0A+%5C+sin++alpha++%2A++frac%7Bcos+alpha+%7D%7Bsin+alpha+%7D++-+cos+alpha++%2B+tg+alpha++%3D+tg+alpha+%0A+%5C+cos+alpha++-+cos+alpha++%2B+tg+alpha+%3D+tg+alpha+%0A%0A)
![\ tg alpha = tg alpha \ tg alpha = tg alpha](https://tex.z-dn.net/?f=+%5C+tg+alpha++%3D+tg+alpha+)
№2 - А
№2 - Б
№3
№4
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