a. $tan2x=-tanx$
$ĐK: \left\{ \begin{array}{l}cos2x \ne 0\\cosx \ne 0\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l}x \ne \dfrac{\pi}{4}+k\dfrac{\pi}{2}\\x \ne \dfrac{\pi}{2}+k\pi \end{array} \right.$
$\Leftrightarrow 2x=-x+k\pi (k \in Z)$
$\Leftrightarrow x=k\dfrac{\pi}{3} (k \in Z)$
b. $cot3x=-cot2x$
$ĐK: \left\{ \begin{array}{l}sin3x \ne 0 \\sin2x \ne 0\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l}x \ne k\dfrac{\pi}{3}\\x\ne k\dfrac{\pi}{2}\end{array} \right.$
$\Leftrightarrow 3x=-2x+k\pi (k \in Z)$
$\Leftrightarrow x=k\dfrac{\pi}{5} (k \in Z)$
c. $cos4x=-cos2x$
$\Leftrightarrow cos4x+cos2x=0$
$\Leftrightarrow 2cos3x.cosx=0$
$\Leftrightarrow \left[ \begin{array}{l}2cos3x=0\\cosx=0\end{array} \right. (k \in Z)$
$\Leftrightarrow \left[ \begin{array}{l}x=\dfrac{\pi}{6}+k\dfrac{\pi}{3}\\x=\dfrac{\pi}{2}+k\pi\end{array} \right. (k \in Z)$
d. $sin3x=-sin2x$
$\Leftrightarrow \left[ \begin{array}{l}3x=-2x+k2\pi=0\\3x=\pi+2x+k2\pi\end{array} \right. (k \in Z)$
$\Leftrightarrow \left[ \begin{array}{l}x=k\dfrac{2\pi}{5} \\x=\pi+k2\pi\end{array} \right. (k \in Z)$
