Toán Lớp 11: giải phương trình 2cos ²x+cos2x=2
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Toán Lớp 11: giải phương trình 2cos ²x+cos2x=2
Comments ( 2 )
2{\cos ^2}x + \cos 2x = 2\\
\Leftrightarrow 2{\cos ^2}x + 2{\cos ^2}x – 1 = 2\\
\Leftrightarrow 4{\cos ^2}x = 3\\
\Leftrightarrow {\cos ^2}x = \dfrac{3}{4}\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = \dfrac{{\sqrt 3 }}{2}\\
\cos x = – \dfrac{{\sqrt 3 }}{2}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{6} + k2\pi \\
x = – \dfrac{\pi }{6} + k2\pi \\
x = \dfrac{{5\pi }}{6} + k2\pi \\
x = – \dfrac{{5\pi }}{6} + k2\pi
\end{array} \right.\left( {k \in \mathbb Z} \right)
\end{array}$