1.
ĐKXĐ: \(cos3x\ne1\)
\(\dfrac{sin3x}{cos3x-1}=0\)
\(\Rightarrow sin3x=0\)
\(\Leftrightarrow sin^23x=0\)
\(\Leftrightarrow cos^23x=1\)
\(\Rightarrow\left[{}\begin{matrix}cos3x=1\left(loại\right)\\cos3x=-1\end{matrix}\right.\)
\(\Rightarrow3x=\pi+k2\pi\)
\(\Rightarrow x=\dfrac{\pi}{3}+\dfrac{k2\pi}{3}\)
2.
ĐKXĐ: \(tanx\ne-\sqrt{3}\Rightarrow x\ne-\dfrac{\pi}{3}+k\pi\)
\(\dfrac{sin2x-1}{tanx+\sqrt{3}}=0\)
\(\Rightarrow sin2x-1=0\)
\(\Leftrightarrow sin2x=1\)
\(\Rightarrow2x=\dfrac{\pi}{2}+k2\pi\)
\(\Rightarrow x=\dfrac{\pi}{4}+k\pi\)
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