Toán Lớp 11: Giải phương trình:
2cos^2x- 2cosx- 2√3sinx.cosx- 1=0
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Toán Lớp 11: Giải phương trình:
2cos^2x- 2cosx- 2√3sinx.cosx- 1=0
GIÚP EM VỚI Ạ!
Comments ( 1 )
2{\cos ^2}x – 2\cos x – 2\sqrt 3 \sin x\cos x – 1 = 0\\
\Leftrightarrow \left( {2{{\cos }^2}x – 1} \right) – 2\sqrt 3 \sin x\cos x = 2\cos x\\
\Leftrightarrow \cos 2x – \sqrt 3 \sin 2x = 2\cos x\\
\Leftrightarrow 2\cos \left( {2x + \dfrac{\pi }{3}} \right) = 2\cos x\\
\Leftrightarrow \cos \left( {2x + \dfrac{\pi }{3}} \right) = \cos x\\
\Leftrightarrow \left[ \begin{array}{l}
2x + \dfrac{\pi }{3} = x + k2\pi \\
2x + \dfrac{\pi }{3} = – x + k2\pi
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = – \dfrac{\pi }{3} + k2\pi \\
x = – \dfrac{\pi }{9} + \dfrac{{k2\pi }}{3}
\end{array} \right.\left( {k \in \mathbb Z} \right)
\end{array}$