Respuesta :

arthurpdc
[tex]\sin(x)-\cos(x)=\sqrt2\\\\ (\sin(x)-\cos(x))^2=(\sqrt2)^2\\\\ \sin^2(x)-2\sin(x)\cos(x)+\cos^2(x)=2\\\\ \underbrace{\sin^2(x)+\cos^2(x)}_{=1}-\underbrace{2\sin(x)\cos(x)}_{=\sin(2x)}=2\\\\ 1-\sin(2x)=2\\\\ \sin(2x)=-1\Longrightarrow 2x=\dfrac{3\pi}{2}+2k\pi,~k\in\mathbb{Z}\\\\\Longrightarrow \boxed{x=\dfrac{3\pi}{4}+k\pi,~k\in\mathbb{Z}}[/tex]

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