Đáp án:
1) $\left\{ \matrix{ x = {\pi \over 4} + {{k\pi } \over 2} \hfill \cr x = k\pi \hfill \cr} \right. (k\in\mathbb Z)$
2) $\left\{ \matrix{ x = {\pi \over 3} + k\pi \hfill \cr x = {\pi \over 2} + k\pi \hfill \cr} \right.\,\,\left( {k \in Z} \right)$
Lời giải:
$\eqalign{ & a)\,\,\cos 2x\tan x = 0 \cr & \text{Đkxđ: }x \ne {\pi \over 2} + k\pi \cr & pt \Leftrightarrow \left[ \matrix{ \cos 2x = 0 \hfill \cr \sin x = 0 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ 2x = {\pi \over 2} + k\pi \hfill \cr x = k\pi \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ x = {\pi \over 4} + {{k\pi } \over 2} \hfill \cr x = k\pi \hfill \cr} \right.\,\,\left( {k\in\mathbb Z} \right) (tm)\cr & b)\,\,\sin 3x\cot x = 0 \cr & \text{Đkxđ: }\sin x \ne 0 \Leftrightarrow x \ne k\pi \cr & pt \Leftrightarrow \left( {3\sin x - 4{{\sin }^3}x} \right){{\cos x} \over {\sin x}} = 0 \cr & \Leftrightarrow \left( {3 - 4{{\sin }^2}x} \right)\cos x = 0 \cr & \Leftrightarrow \left( {3 - 2\left( {1 - \cos 2x} \right)} \right)\cos x = 0 \cr & \Leftrightarrow \left( {2\cos 2x + 1} \right)\cos x = 0 \cr & \Leftrightarrow \left[ \matrix{ \cos 2x = - {1 \over 2} \hfill \cr \cos x = 0 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ 2x = {{2\pi } \over 3} + k2\pi \hfill \cr x = {\pi \over 2} + k\pi \hfill \cr} \right. \cr & \Leftrightarrow \left[ \matrix{ x = {\pi \over 3} + k\pi \hfill \cr x = {\pi \over 2} + k\pi \hfill \cr} \right.\,\,\left( {k \in Z} \right)\,\,\left( {tm} \right) \cr} $
