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$$\eqalign{ & \tan 3x.\tan x = 1\,\,\left( {DK:\,\,\cos 3x \ne 0;\,\,\cos x \ne 0} \right) \cr & \Leftrightarrow \tan 3x = {1 \over {\tan x}} \cr & \Leftrightarrow \tan 3x = \cot x = \tan \left( {{\pi \over 2} - x} \right) \cr & \Leftrightarrow 3x = {\pi \over 2} - x + k\pi \cr & \Leftrightarrow 4x = {\pi \over 2} + k\pi \Leftrightarrow x = {\pi \over 8} + {{k\pi } \over 4}\,\,\left( {k \in Z} \right)\,\,\left( {tm} \right) \cr} $$
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