sinx+cosx=1⇔$\sqrt{2}$ sin(x+$\frac{\pi}{4}$ )=1
⇔ sin(x+$\frac{\pi}{4}$ )=$\frac{1}{\sqrt{2}}$ =sin$\frac{\pi}{4}$
⇔$\left[\begin{matrix} x+\frac{\pi}{4}=\frac{\pi}{4}+k2\pi\\ x+\frac{\pi}{4}=\frac{3\pi}{4}+k2\pi\end{matrix}\right.$
⇔\(\left[ \begin{array}{l}x=k2\pi\\x=\frac{\pi}{2}+k2\pi\end{array} \right.\) (k∈Z)
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