Toán Lớp 11: Giải pt đẳng cấp
4sin³x+3cos²x-3sinx-sin²x.cosx=0
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Toán Lớp 11: Giải pt đẳng cấp
4sin³x+3cos²x-3sinx-sin²x.cosx=0
Comments ( 1 )
4{\sin ^3}x + 3{\cos ^3}x – 3xinx – {\sin ^2}x \times \cos x = 0\\
\Rightarrow 4{\tan ^3}x + 3 – \frac{{3\sin x}}{{{{\cos }^3}x}} – \frac{{{{\sin }^2}x \times \cos x}}{{{{\cos }^3}x}} = 0\\
\Rightarrow 4{\tan ^3}x + 3 – 3\tan x\left( {1 + {{\tan }^2}x} \right) – {\tan ^2}x = 0\\
\Rightarrow 4{\tan ^3}x + 3 – 3\tan x – 3ta{n^3}x + 3 = 0\\
\Rightarrow {\tan ^3} – {\tan ^2}x – 3\tan x + 3 = 0\\
\Rightarrow \left[ \begin{array}{l}
\tan x = 1\\
\tan x = \sqrt 3 \\
\tan x = – \sqrt 3
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x = \frac{\pi }{4} + k\pi \\
x = \frac{\pi }{3} + k\pi \\
x = \frac{\pi }{3} + k\pi
\end{array} \right.
\end{array}\]