Ctg (a/2) = 1/2; tg (a/2) = 2
![sin(a)= \frac{2tg(a/2)}{1+tg^2(a/2)} = \frac{2*2}{1+2^2}= \frac{4}{5};cos(a)= \frac{1-tg^2(a/2)}{1+tg^2(a/2)}= \frac{1-2^2}{1+2^2}= -\frac{3}{5}](https://tex.z-dn.net/?f=sin%28a%29%3D+%5Cfrac%7B2tg%28a%2F2%29%7D%7B1%2Btg%5E2%28a%2F2%29%7D+%3D+%5Cfrac%7B2%2A2%7D%7B1%2B2%5E2%7D%3D+%5Cfrac%7B4%7D%7B5%7D%3Bcos%28a%29%3D+%5Cfrac%7B1-tg%5E2%28a%2F2%29%7D%7B1%2Btg%5E2%28a%2F2%29%7D%3D+%5Cfrac%7B1-2%5E2%7D%7B1%2B2%5E2%7D%3D+-%5Cfrac%7B3%7D%7B5%7D+)
Подставляем в наше выражение
![\frac{14sin(a)+21cos(a)}{cos(a)-sin(a)}= \frac{14*4/5+21*(-3/5)}{-3/5-4/5}= \frac{56/5-63/5}{-7/5} = \frac{-7}{-7} =1](https://tex.z-dn.net/?f=+%5Cfrac%7B14sin%28a%29%2B21cos%28a%29%7D%7Bcos%28a%29-sin%28a%29%7D%3D+%5Cfrac%7B14%2A4%2F5%2B21%2A%28-3%2F5%29%7D%7B-3%2F5-4%2F5%7D%3D+%5Cfrac%7B56%2F5-63%2F5%7D%7B-7%2F5%7D+%3D+%5Cfrac%7B-7%7D%7B-7%7D+%3D1)
348:2=174-в детский сад
174:3=58-яблок израсходвали на варенье
1) 15*3=45(руб)-Потратила на огурцы
2) 15*2=30(руб)-Потратила на помидоры
3) 45+30=75(руб)-Потратила всего
4) 100-75=25(руб)
Ответ:У хозяйки осталось 25 рублей