<s>[INST] Solving $\cos x+\sin x-1=0$ How does one solve this equation?

$$\cos {x}+\sin {x}-1=0$$

I have no idea how to start it.
Can anyone give me some hints? Is there an identity for $\cos{x}+\sin{x}$?
Thanks in advance!
 [/INST] As $\sin\left(x+\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2}\left(\cos x+\sin x\right)$ by the angle addition formula we find that:
\begin{equation}
\begin{aligned}
\cos x+\sin x-1&=0\\
\implies\sqrt{2}\sin\left(x+\frac{\pi}{4}\right)&=1\\
\implies\sin\left(x+\frac{\pi}{4}\right)&=\frac{\sqrt{2}}{2}\\
\implies x+\frac{\pi}{4}&=\frac{\pi}{4}+2\pi n,\frac{3\pi}{4}+2\pi n\\
\implies x&=2\pi n,\frac{\pi}{2}+2\pi n
\end{aligned}
\end{equation}
for $n\in\mathbb{Z}$.
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