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\displaystyle [br]\begin{equation*}\sin x + \cos x = \sqrt{2}\sin \left(x - \frac{\pi}{4}\right)\end{equation*}
x + \frac{\pi}{4} \in \left[\frac{\pi}{4}, \frac{3\pi}{4}\right] \union \left[\frac{5\pi}{4}, \frac{7\pi}{4}\right]
\displaystyle [br]\begin{equation*}\sin x + \cos x = \sqrt{2}\sin \left(x - \frac{\pi}{4}\right)\end{equation*}
x + \frac{\pi}{4} \in \left[\frac{\pi}{4}, \frac{3\pi}{4}\right] \union \left[\frac{5\pi}{4}, \frac{7\pi}{4}\right]
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