Toán Lớp 11: sin bình x + 3 sinx x cosx = 1
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Toán Lớp 11: sin bình x + 3 sinx x cosx = 1
Comments ( 1 )
{\sin ^2}x + 3\sin x\cos x = 1\\
\Leftrightarrow {\sin ^2}x – 1 + 3\sin x\cos x = 0\\
\Leftrightarrow 3\sin x\cos x – {\cos ^2}x = 0\\
\Leftrightarrow \cos x\left( {3\sin x – \cos x} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = 0\\
3\sin x – \cos x = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{2} + k\pi \\
\dfrac{3}{{\sqrt {10} }}\sin x – \dfrac{1}{{\sqrt {10} }}\cos x = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{2} + k\pi \\
\sin \left( {x – \alpha } \right) = 0
\end{array} \right.\left( {\alpha = \arccos \dfrac{3}{{\sqrt {10} }}} \right)\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{2} + k\pi \\
x = \alpha + k\pi
\end{array} \right.\left( {k \in \mathbb Z} \right)
\end{array}$