основание (3) больше единицы...
знак неравенства сохраняется...
5х - 2.5 ≤ 0.5
5х ≤ 3
х ≤ 3/5
х ≤ 0.6
Есть такие формулы преобразования произведения в сумму:
sin a*sin b = 1/2*(cos(a-b) - cos(a+b))
sin a*cos b = 1/2*(sin(a+b) + sin(a-b))
Умножаем по порядку
1)
![sin \frac{x-y}{2}sin \frac{y-z}{2}= \frac{1}{2}(cos \frac{x-y-y+z}{2} -cos \frac{x-y+y-z}{2} )=](https://tex.z-dn.net/?f=sin+%5Cfrac%7Bx-y%7D%7B2%7Dsin+%5Cfrac%7By-z%7D%7B2%7D%3D+%5Cfrac%7B1%7D%7B2%7D%28cos+%5Cfrac%7Bx-y-y%2Bz%7D%7B2%7D+-cos+%5Cfrac%7Bx-y%2By-z%7D%7B2%7D+%29%3D)
![= \frac{1}{2} (cos \frac{x-2y+z}{2} -cos \frac{x-z}{2} )](https://tex.z-dn.net/?f=%3D+%5Cfrac%7B1%7D%7B2%7D+%28cos+%5Cfrac%7Bx-2y%2Bz%7D%7B2%7D+-cos+%5Cfrac%7Bx-z%7D%7B2%7D+%29)
2)
![sin \frac{z-x}{2}*\frac{1}{2} (cos \frac{x-2y+z}{2} -cos \frac{x-z}{2} )= \frac{1}{2}(sin \frac{z-x}{2}cos \frac{x-2y+z}{2}-](https://tex.z-dn.net/?f=sin+%5Cfrac%7Bz-x%7D%7B2%7D%2A%5Cfrac%7B1%7D%7B2%7D+%28cos+%5Cfrac%7Bx-2y%2Bz%7D%7B2%7D+-cos+%5Cfrac%7Bx-z%7D%7B2%7D+%29%3D+%5Cfrac%7B1%7D%7B2%7D%28sin+%5Cfrac%7Bz-x%7D%7B2%7Dcos+%5Cfrac%7Bx-2y%2Bz%7D%7B2%7D-)
![-sin \frac{z-x}{2}cos \frac{x-z}{2}) = \frac{1}{4}(sin \frac{z-x+x-2y+z}{2}+sin \frac{z-x-x+2y-z}{2}- sin \frac{2z-2x}{2})](https://tex.z-dn.net/?f=-sin+%5Cfrac%7Bz-x%7D%7B2%7Dcos+%5Cfrac%7Bx-z%7D%7B2%7D%29+%3D+%5Cfrac%7B1%7D%7B4%7D%28sin+%5Cfrac%7Bz-x%2Bx-2y%2Bz%7D%7B2%7D%2Bsin+%5Cfrac%7Bz-x-x%2B2y-z%7D%7B2%7D-+sin+%5Cfrac%7B2z-2x%7D%7B2%7D%29+)
![= \frac{1}{4}(sin(z-y)+sin(y-x)-sin(z-x))= \frac{1}{4}](https://tex.z-dn.net/?f=%3D+%5Cfrac%7B1%7D%7B4%7D%28sin%28z-y%29%2Bsin%28y-x%29-sin%28z-x%29%29%3D+%5Cfrac%7B1%7D%7B4%7D+)
Умножаем все на 4
sin(z-y) + sin(y-x) - sin(z-x) = -sin(x-y) - sin(y-z) - sin(z-x) = 1
Меняем знак
sin(x-y) + sin(y-z) + sin(z-x) = -1
А) 8*5=40
40*4=160
160\8=20
В 20 раз
Б) Пусть число будет х
х*4*5=4х5=20х
В 20 раз