Answer
$x=\{\frac{3\pi}{4}\}$
Work Step by Step
$sin(x)-cos(x)=\sqrt{2}$
$(sin(x)-cos(x))^2=(\sqrt{2})^2\;\;\;\;\;\;\;\;\;\;$
$sin^2(x)-2sin(x)cos(x)+cos^2(x)=2\;\;\;\;\;\;\;\;\;\;\;\;$
$-2sin(x)cos(x)+1=2$
$-sin(2x)=1$
$sin(2x)=-1$
$2x= sin^{-1}(-1)$
$2x=\frac{3\pi}{2}\;\;\;\;\;\;\;\;\;\;\;\;\;\;$ Divided each side by $2$
$x=\frac{3\pi}{4}$
$x=\{\frac{3\pi}{4}\}$
