## [Toán 11] 3tan3x+cot3x-4=0 Giúp em với ạ

Question

[Toán 11]
3tan3x+cot3x-4=0
Giúp em với ạ

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3 tuần 2021-08-21T16:49:57+00:00 2 Answers 2 views 0

$$\left[ \matrix{ x = {\pi \over {12}} + {{k\pi } \over 3} \hfill \cr x = {1 \over 3}\arctan {1 \over 3} + {{k\pi } \over 3} \hfill \cr} \right.\,\,\left( {k \in Z} \right)$$
\eqalign{ & 3\tan 3x + \cot 3x – 4 = 0 \cr & DK:\,\,3x \ne k\pi \Leftrightarrow x \ne {{k\pi } \over 3}\,\,\left( {k \in Z} \right) \cr & Pt \Leftrightarrow 3\tan 3x + {1 \over {\tan 3x}} – 4 = 0 \cr & \Leftrightarrow 3{\tan ^2}3x – 4\tan 3x + 1 = 0 \cr & \Leftrightarrow \left[ \matrix{ \tan 3x = 1 \hfill \cr \tan 3x = {1 \over 3} \hfill \cr} \right. \cr & \Leftrightarrow \left[ \matrix{ 3x = {\pi \over 4}k\pi \hfill \cr 3x = \arctan {1 \over 3} + k\pi \hfill \cr} \right. \cr & \Leftrightarrow \left[ \matrix{ x = {\pi \over {12}} + {{k\pi } \over 3} \hfill \cr x = {1 \over 3}\arctan {1 \over 3} + {{k\pi } \over 3} \hfill \cr} \right.\,\,\left( {k \in Z} \right) \cr}