Toán Lớp 11: 3 sin2x – căn3 cos2x = 3
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Toán Lớp 11: 3 sin2x – căn3 cos2x = 3
làm sao vậy ạ giúp e vs
Comments ( 1 )
\quad 3\sin2x – \sqrt3\cos2x = 3\\
\Leftrightarrow \dfrac{\sqrt3}{2}\sin2x – \dfrac12\cos2x = \dfrac{\sqrt3}{2}\\
\Leftrightarrow \sin\left(2x – \dfrac{\pi}{6}\right) = \sin\dfrac{\pi}{3}\\
\Leftrightarrow \left[\begin{array}{l}2x – \dfrac{\pi}{6} = \dfrac{\pi}{3} + k2\pi\\2x – \dfrac{\pi}{6} = \dfrac{2\pi}{3} + k2\pi\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = \dfrac{\pi}{4} + k\pi\\x = \dfrac{5\pi}{12} + k\pi\end{array}\right.\quad (k\in\Bbb Z)\\
\text{Vậy}\ S = \left\{x = \dfrac{\pi}{4} + k\pi;\ \dfrac{5\pi}{12} + k\pi\ \Bigg|\ k\in\Bbb Z\right\}
\end{array}\)