نکته: $\operatorname{Sin}\alpha \pm \operatorname{Cos}\alpha =\sqrt{2}\operatorname{Sin}(\alpha \pm \frac{\pi }{4})$  بنابر نکته‌ی فوق داریم: $\operatorname{Sin}x+\operatorname{Cos}x=1\Rightarrow \sqrt{2}\operatorname{Sin}(x+\frac{\pi }{4})=1\Rightarrow \operatorname{Sin}(x+\frac{\pi }{4})=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}\Rightarrow \operatorname{Sin}(x+\frac{\pi }{4})=\operatorname{Sin}\frac{\pi }{4}\Rightarrow \left\{ _{x+\frac{\pi }{4}=2k\pi +\pi -\frac{\pi }{4}}^{x+\frac{\pi }{4}=2k\pi +\frac{\pi }{4}}\Rightarrow \left\{ _{x=2k\pi +\frac{\pi }{2}}^{x=2k\pi } \right. \right.$