Toán Lớp 11: giúp mình với
Giải Pt: 3Cosx+Cos2x-Cos3x+1=2Sinx*Sin2x
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Toán Lớp 11: giúp mình với
Giải Pt: 3Cosx+Cos2x-Cos3x+1=2Sinx*Sin2x
Comments ( 1 )
3\cos x + \cos 2x – \cos 3x + 1 = 2\sin x\sin 2x\\
\Leftrightarrow 3\cos x + \cos 2x – \cos 3x + 1 = \cos x – \cos 3x\\
\Leftrightarrow 3\cos x + \cos 2x + 1 = \cos x\\
\Leftrightarrow 2\cos x + \cos 2x + 1 = 0\\
\Leftrightarrow 2\cos x + 2{\cos ^2}x – 1 + 1 = 0\\
\Leftrightarrow 2\cos x + 2{\cos ^2}x = 0\\
\Leftrightarrow 2\cos x\left( {\cos x + 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = 0\\
\cos x = – 1
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{2} + k\pi \\
x = \pi + k2\pi
\end{array} \right.\left( {k \in \mathbb Z} \right)
\end{array}$