Sina+sinb=2sin((a+b)/2)cos((a-b)/2)
Sin2a+sin4a=2sin3acosa
Cosa+cosb=2cos((a+b)/2)cos((a-b)/2)
Cos2a+cos4a=2cos3acosa
Теперь
(2sin3acosa)^2+(2cos3acosa)^2=4sin^23acos^2a+4cos^23acos^2a=4cos^2a(cos^23a+sin^23a
Sin^2a+cos^2a=1
Все доказано
Решениееееееееееееееееееее
![\frac{4x+3y}{4x-3y}=\frac{4*(-\frac{3}{4})+3*(-\frac{1}{6})}{4*(-\frac{3}{4})-3*(-\frac{1}{6})}=\frac{-3-\frac{1}{2} }{-3+\frac{1}{2} }=\frac{-3,5}{-2,5}=1,4](https://tex.z-dn.net/?f=%5Cfrac%7B4x%2B3y%7D%7B4x-3y%7D%3D%5Cfrac%7B4%2A%28-%5Cfrac%7B3%7D%7B4%7D%29%2B3%2A%28-%5Cfrac%7B1%7D%7B6%7D%29%7D%7B4%2A%28-%5Cfrac%7B3%7D%7B4%7D%29-3%2A%28-%5Cfrac%7B1%7D%7B6%7D%29%7D%3D%5Cfrac%7B-3-%5Cfrac%7B1%7D%7B2%7D+%7D%7B-3%2B%5Cfrac%7B1%7D%7B2%7D+%7D%3D%5Cfrac%7B-3%2C5%7D%7B-2%2C5%7D%3D1%2C4)
2a)
- 2(2b - 3) + 4(3b - 2) = - 4b + 6 + 12b - 8 = 8b - 2
б)
15a - (a + 3) + (2a - 1)= 15a - a - 3 + 2a - 1 = 16a - 4
в)
5a - (6a - (7a - (8a - 9))) = 5a - (6a - (7a - 8a + 9)) = 5a - (6a + a - 9) = 5a - (7a - 9)=
= 5a - 7a + 9 = 9 - 2a
3)
- 2(3,5y - 2,5) + 4,5y - 1 = - 7y + 5 + 4,5y - 1 = - 2,5y + 4
- 2,5 * 4/5 + 4 = - 2 + 4 = 2
Решаем систему двух уравнений с двумя переменными
![\left \{ {{x-y=-1} \atop {2x+y=4}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx-y%3D-1%7D+%5Catop+%7B2x%2By%3D4%7D%7D+%5Cright.+)
Складываем уравнения и записываем сумму уравнений вместо второго уравнения
![\left \{ {{x-y=-1} \atop {3x=3}} \right. \\ \\ \left \{ {{y=x+1} \atop {x=1}} \right. \\ \\ \left \{ {{y=1+1} \atop {x=1}} \right. \\ \\ \left \{ {{y=2} \atop {x=1}} \right. \\](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx-y%3D-1%7D+%5Catop+%7B3x%3D3%7D%7D+%5Cright.+%5C%5C++%5C%5C++%5Cleft+%5C%7B+%7B%7By%3Dx%2B1%7D+%5Catop+%7Bx%3D1%7D%7D+%5Cright.+%5C%5C++%5C%5C+%5Cleft+%5C%7B+%7B%7By%3D1%2B1%7D+%5Catop+%7Bx%3D1%7D%7D+%5Cright.+%5C%5C++%5C%5C++%5Cleft+%5C%7B+%7B%7By%3D2%7D+%5Catop+%7Bx%3D1%7D%7D+%5Cright.+%5C%5C++)
Ответ. (1;2)