Toán Lớp 11: 2cot2x+tan2x=3 . Giải chi tiết giúp mình với ạ
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Toán Lớp 11: 2cot2x+tan2x=3 . Giải chi tiết giúp mình với ạ
Comments ( 1 )
x = \arctan 2 + k\pi \\
x = \dfrac{\pi }{4} + k\pi
\end{array} \right.\)
DK:\left\{ \begin{array}{l}
\sin 2x \ne 0\\
\cos 2x \ne 0
\end{array} \right.\\
\to \sin 4x \ne 0\\
\to 4x \ne k\pi \\
\to x \ne \dfrac{{k\pi }}{4}\left( {k \in Z} \right)\\
2\cot 2x + \tan 2x = 3\\
\to \dfrac{2}{{\tan 2x}} + \tan 2x = 3\\
\to {\tan ^2}2x – 3\tan x + 2 = 0\\
\to \left( {\tan x – 2} \right)\left( {\tan x – 1} \right) = 0\\
\to \left[ \begin{array}{l}
\tan x = 2\\
\tan x = 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \arctan 2 + k\pi \\
x = \dfrac{\pi }{4} + k\pi
\end{array} \right.\left( {k \in Z} \right)
\end{array}\)