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Ответ:
![x_1=2\pi n, n \in Z\\x_2=\frac{3\pi}{2}+2\pi k, k \in Z](https://tex.z-dn.net/?f=x_1%3D2%5Cpi%20n%2C%20n%20%5Cin%20Z%5C%5Cx_2%3D%5Cfrac%7B3%5Cpi%7D%7B2%7D%2B2%5Cpi%20k%2C%20k%20%5Cin%20Z)
Объяснение:
Преобразуем левую часть уравнения:
![cos(x)-sin(x)=\sqrt{1^2+1^2}*(\frac{1}{\sqrt{1^2+1^2}}cos(x)-\frac{1}{\sqrt{1^2+1^2}}sin(x))=\sqrt{2}(sin(\frac{\pi}{4})cos(x)-cos(\frac{\pi}{4})sin(x))=\sqrt{2}sin(\frac{\pi}{4}-x)](https://tex.z-dn.net/?f=cos%28x%29-sin%28x%29%3D%5Csqrt%7B1%5E2%2B1%5E2%7D%2A%28%5Cfrac%7B1%7D%7B%5Csqrt%7B1%5E2%2B1%5E2%7D%7Dcos%28x%29-%5Cfrac%7B1%7D%7B%5Csqrt%7B1%5E2%2B1%5E2%7D%7Dsin%28x%29%29%3D%5Csqrt%7B2%7D%28sin%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29cos%28x%29-cos%28%5Cfrac%7B%5Cpi%7D%7B4%7D%29sin%28x%29%29%3D%5Csqrt%7B2%7Dsin%28%5Cfrac%7B%5Cpi%7D%7B4%7D-x%29)
Отсюда получим уравнение:
![\sqrt{2}sin(\frac{\pi}{4}-x)=1\\sin(\frac{\pi}{4}-x)=\frac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7Dsin%28%5Cfrac%7B%5Cpi%7D%7B4%7D-x%29%3D1%5C%5Csin%28%5Cfrac%7B%5Cpi%7D%7B4%7D-x%29%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
Найдем общее решение уравнения.
![sin(\frac{\pi}{4}-x)=\frac{\sqrt{2}}{2}\\sin(x-\frac{\pi}{4})=-\frac{\sqrt{2}}{2}\\x-\frac{\pi}{4}=(-1)^narcsin(-\frac{\sqrt{2}}{2})+\pi n\\x=\frac{\pi}{4}+(-1)^{n+1}\frac{\pi}{4}+\pi n, n \in Z](https://tex.z-dn.net/?f=sin%28%5Cfrac%7B%5Cpi%7D%7B4%7D-x%29%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5C%5Csin%28x-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5C%5Cx-%5Cfrac%7B%5Cpi%7D%7B4%7D%3D%28-1%29%5Enarcsin%28-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29%2B%5Cpi%20n%5C%5Cx%3D%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%28-1%29%5E%7Bn%2B1%7D%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cpi%20n%2C%20n%20%5Cin%20Z)
Или же можно записать так:
![x_1=2\pi n, n \in Z\\x_2=\frac{3\pi}{2}+2\pi k, k \in Z](https://tex.z-dn.net/?f=x_1%3D2%5Cpi%20n%2C%20n%20%5Cin%20Z%5C%5Cx_2%3D%5Cfrac%7B3%5Cpi%7D%7B2%7D%2B2%5Cpi%20k%2C%20k%20%5Cin%20Z)
1), 3),4),6) это точки лежащие между точками А и N
2, можно представить как 1+1, а 1 - как 0.5 + 0.5. Тогда получим
f(2) = f(1 + 1) = f(1) + f(1) + 100 = 2f(1) + 100 = 2f(0.5 + 0.5) + 100 = 2(f(0.5) + f(0.5) + 25) + 100 = 2(10 + 10 + 25) + 100 = 2 * 45 + 100 = 90 + 100 = 190
<span>Решение
3 вариант а,б,в,г
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