Toán Lớp 11: phương trình (sinx +1)(2 cos 2x -√2)=0 có nghiệm là ?
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Toán Lớp 11: phương trình (sinx +1)(2 cos 2x -√2)=0 có nghiệm là ?
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\quad (\sin x + 1)\left(2\cos2x – \sqrt2\right) =0\\
\Leftrightarrow \left[\begin{array}{l}\sin x = -1\\\cos2x= \dfrac{\sqrt2}{2}\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = – \dfrac{\pi}{2} + k2\pi\\2x = – \dfrac{\pi}{4} + k2\pi\\2x = \dfrac{\pi}{4} + k2\pi\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = – \dfrac{\pi}{2} + k2\pi\\x = – \dfrac{\pi}{8} + k\pi\\x = \dfrac{\pi}{8} + k\pi\end{array}\right.\quad (k\in\Bbb Z)\\
\text{Vậy}\ S = \left\{- \dfrac{\pi}{2} + k2\pi;\ – \dfrac{\pi}{8} + k\pi;\ \dfrac{\pi}{8} + k\pi\ \Bigg|\ k\in\Bbb Z\right\}
\end{array}\)