Toán Lớp 11: sin2x – 2cosx + √3 cos2x = 0
Giúp em với ạ : Giải phương trình ạ
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Toán Lớp 11: sin2x – 2cosx + √3 cos2x = 0
Giúp em với ạ : Giải phương trình ạ
Comments ( 2 )
\quad \sin2x – 2\cos x + \sqrt3\cos2x =0\\
\Leftrightarrow \dfrac{\sqrt3}{2}\cos2x +\dfrac12\sin2x =\cos x\\
\Leftrightarrow \cos\left(2x – \dfrac{\pi}{6}\right) = \cos x\\
\Leftrightarrow \left[\begin{array}{l}2x – \dfrac{\pi}{6} = – x + k2\pi\\2x – \dfrac{\pi}{6} = x + k2\pi\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x= \dfrac{\pi}{18} + \dfrac{k2\pi}{3}\\x = \dfrac{\pi}{6} + k2\pi\end{array}\right.\quad (k\in\Bbb Z)\\
\text{Vậy}\ S = \left\{\dfrac{\pi}{18} + \dfrac{k2\pi}{3};\ \dfrac{\pi}{6} + k2\pi\ \Bigg|\ k\in\Bbb Z\right\}
\end{array}\)