Question

cot3x=tan2x

Answer 1

cot3x = tan2x

đkxđ: \(\left\{{}\begin{matrix}sin3x\ne0\\cos2x\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{k\pi}{3}\\x\ne\frac{\pi}{4}+\frac{k\pi}{2}\end{matrix}\right.\)(k\(\in\)Z)

\(\Leftrightarrow\frac{cos3x}{sin3x}=\frac{sin2x}{cos2x}\)

\(\Leftrightarrow cos3x.cos2x=sin3x.sin2x\)

\(\Leftrightarrow cos3x.cos2x-sin3x.sin2x=0\)

\(\Leftrightarrow cos\left(3x+2x\right)=0\)

<=> \(5x=\frac{\pi}{2}+k\pi\)

<=> \(x=\frac{\pi}{10}+\frac{k\pi}{5}\)