![image](https://tex.z-dn.net/?f=1%29cosx-sinx%3D-2%5C%3B+net%5C%3B+reshenij%2C%5C%5C%5C%5Ctak%5C%3B+kak%5C%3B+iz%5C%3B+OOF%3Acosx-sinx-1%3E0%5C%3B+%5Cto+cosx-sinx%3E1%5C%5C%5C%5C2%29cosx-sinx%3D1%7C%3A%5Csqrt2%5C%5C%5C%5C%5Cfrac%7B1%7D%7B%5Csqrt2%7Dcosx-%5Cfrac%7B1%7D%7B%5Csqrt2%7Dsinx%3D%5Cfrac%7B1%7D%7B%5Csqrt2%7D%5C%5C%5C%5Csin%5Cfrac%7B%5Cpi%7D%7B4%7Dcosx-cos%5Cfrac%7B%5Cpi%7D%7B4%7Dsinx%3D%5Cfrac%7B1%7D%7B%5Csqrt2%7D%5C%5C%5C%5Csin%28%5Cfrac%7B%5Cpi%7D%7B4%7D-x%29%3D%5Cfrac%7B1%7D%7B%5Csqrt2%7D%5C%3B+%5Cto+%5C%3B+sin%28x-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%3D-%5Cfrac%7B1%7D%7B%5Csqrt2%7D+%5C%5C%5C%5Cx-%5Cfrac%7B%5Cpi%7D%7B4%7D%3D%28-1%29%5E%7Bn%2B1%7D%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cpi+n%2C%5C%3B+n%5Cin+Z%5C%5C%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+n%3D%5Cfrac%7B%5Cpi%7D%7B4%7D%28%28-1%29%5E%7Bn%2B1%7D%2B1%29%2B%5Cpi+n)
0\; \to cosx-sinx>1\\\\2)cosx-sinx=1|:\sqrt2\\\\\frac{1}{\sqrt2}cosx-\frac{1}{\sqrt2}sinx=\frac{1}{\sqrt2}\\\\sin\frac{\pi}{4}cosx-cos\frac{\pi}{4}sinx=\frac{1}{\sqrt2}\\\\sin(\frac{\pi}{4}-x)=\frac{1}{\sqrt2}\; \to \; sin(x-\frac{\pi}{4})=-\frac{1}{\sqrt2} \\\\x-\frac{\pi}{4}=(-1)^{n+1}\frac{\pi}{4}+\pi n,\; n\in Z\\\\x=\frac{\pi}{4}+(-1)^{n+1}\frac{\pi}{4}+\pi n=\frac{\pi}{4}((-1)^{n+1}+1)+\pi n" alt="1)cosx-sinx=-2\; net\; reshenij,\\\\tak\; kak\; iz\; OOF:cosx-sinx-1>0\; \to cosx-sinx>1\\\\2)cosx-sinx=1|:\sqrt2\\\\\frac{1}{\sqrt2}cosx-\frac{1}{\sqrt2}sinx=\frac{1}{\sqrt2}\\\\sin\frac{\pi}{4}cosx-cos\frac{\pi}{4}sinx=\frac{1}{\sqrt2}\\\\sin(\frac{\pi}{4}-x)=\frac{1}{\sqrt2}\; \to \; sin(x-\frac{\pi}{4})=-\frac{1}{\sqrt2} \\\\x-\frac{\pi}{4}=(-1)^{n+1}\frac{\pi}{4}+\pi n,\; n\in Z\\\\x=\frac{\pi}{4}+(-1)^{n+1}\frac{\pi}{4}+\pi n=\frac{\pi}{4}((-1)^{n+1}+1)+\pi n" align="absmiddle" class="latex-formula">