Toán Lớp 11: Giải pt: cos2x-√3sin2x=2cosx
giúp m với :((((
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Toán Lớp 11: Giải pt: cos2x-√3sin2x=2cosx
giúp m với :((((
Comments ( 2 )
\cos 2x – \sqrt 3 \sin 2x = 2\cos x\\
\Leftrightarrow 2\left( {\dfrac{1}{2}\cos 2x – \dfrac{{\sqrt 3 }}{2}\sin 2x} \right) = 2\cos x\\
\Leftrightarrow \cos \dfrac{\pi }{3}\cos 2x – \sin \dfrac{\pi }{3}\sin 2x = \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.\\
\Leftrightarrow \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}$