Toán Lớp 11: Giúp m với
Giải pt: cosx – cân 3sinx = -1
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Toán Lớp 11: Giúp m với
Giải pt: cosx – cân 3sinx = -1
Comments ( 1 )
\cos x – \sqrt 3 \sin x = – 1\\
\Leftrightarrow \dfrac{1}{2}\cos x – \dfrac{{\sqrt 3 }}{2}\sin x = – \dfrac{1}{2}\\
\Leftrightarrow \sin \dfrac{\pi }{6}.\cos x – \cos \dfrac{\pi }{6}.\sin x = – \dfrac{1}{2}\\
\Leftrightarrow \sin \left( {\dfrac{\pi }{6} – x} \right) = \sin – \dfrac{\pi }{6}\\
\Leftrightarrow \left[ \begin{array}{l}
\dfrac{\pi }{6} – x = \dfrac{{ – \pi }}{6} + k2\pi \\
\dfrac{\pi }{6} – x = \pi + \dfrac{\pi }{6} + k2\pi
\end{array} \right.\left( {k \in Z} \right)\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{3} – k2\pi \\
x = – \pi – k2\pi
\end{array} \right.\left( {k \in Z} \right)\\
Vậy\,\left[ \begin{array}{l}
x = \dfrac{\pi }{3} – k2\pi \\
x = – \pi – k2\pi
\end{array} \right.\left( {k \in Z} \right)
\end{array}$