[m]cosx=sin(\frac{π}{2}-x)[/m]
[m]sinx-sin(\frac{π}{2}-x)=2[/m]
[m]2sin\frac{x-(\frac{π}{2}-x)}{2}\cdot cos\frac{x+(\frac{π}{2}-x)}{2}=2[/m]
[m]2sin(x-\frac{π}{4})\cdot cos\frac{π}{4}=2[/m]
[m]2sin(x-\frac{π}{4})\cdot \frac{\sqrt{2}}{2}=2[/m]
[m]sin(x-\frac{π}{4})=\sqrt{2}[/m] не имеет корней
[m]\sqrt{2} > 1[/m], а
[m]|sin(x-\frac{π}{4})| ≤1[/m]