معادله را ساده می‌کنیم. داریم:

$\left\{ \begin{matrix}\operatorname{Sin}(x-\frac{\pi }{4})=\frac{\sqrt{2}}{2}(\operatorname{Sin}x-\operatorname{Cos}x)  \\\operatorname{Sin}(x+\frac{\pi }{4})=\frac{\sqrt{2}}{2}(\operatorname{Sin}x+\operatorname{Cos}x)  \\\end{matrix} \right.\Rightarrow ({{\operatorname{Sin}}^{2}}x-{{\operatorname{Cos}}^{2}}x)=\frac{1}{2}\Rightarrow {{\operatorname{Cos}}^{2}}x-{{\operatorname{Sin}}^{2}}x=-\frac{1}{2}\Rightarrow \operatorname{Cos}2x=-\frac{1}{2}=\operatorname{Cos}\frac{2\pi }{3}\Rightarrow \left\{ \begin{matrix}2x=2k\pi +\frac{2\pi }{3}  \\2x=2k\pi -\frac{2\pi }{3}  \\\end{matrix}\Rightarrow x=k\pi \pm \frac{\pi }{3} \right.$