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">