Toán Lớp 11: Nghiệm của phương trình : sin x + cos x =1 là
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Toán Lớp 11: Nghiệm của phương trình : sin x + cos x =1 là
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\quad \sin x + \cos x = 1\\
\Leftrightarrow \sqrt2\sin\left(x + \dfrac{\pi}{4}\right) = 1\\
\Leftrightarrow \sin\left(x + \dfrac{\pi}{4}\right) =\dfrac{\sqrt2}{2}\\
\Leftrightarrow \left[\begin{array}{l}x + \dfrac{\pi}{4} = \dfrac{\pi}{4} + k2\pi\\x + \dfrac{\pi}{4} = \dfrac{3\pi}{4} + k2\pi\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x=k2\pi\\x = \dfrac{\pi}{2} + k2\pi\end{array}\right.\quad (k\in\Bbb Z)\\
\text{Vậy}\ S = \left\{k2\pi;\ \dfrac{\pi}{2} + k2\pi\ \Bigg|\ k\in\Bbb Z\right\}
\end{array}\)