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Đk: $\left \{\begin{array}{l} \cos (2x+1)\ne0\\ \sin x\ne 0 \end{array} \right .(k\in\mathbb Z)$ $\tan(2x+1)+\cot x=0$ $\Rightarrow \dfrac{\sin(2x+1)}{\cos (2x+1)}+\dfrac{\cos x}{\sin x}=0$ $\Rightarrow \sin(2x+1)\sin x+\cos x\cos (2x+1)=0$ $\Rightarrow \cos (x+1)=0$ $\Rightarrow x+1=\dfrac{\pi}{2}+k\pi$ $\Rightarrow x=-1+\dfrac{\pi}{2}+k\pi(k\in\mathbb Z)$
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