Question

Cotx = tanx + 2tanx

giúp ạ gấp gấp!!!

Answer 1

Đề??

ĐK: \(x\ne\dfrac{k\pi}{2}\)

\(cotx=tanx+2tanx\)

\(\Leftrightarrow cotx=3tanx\)

\(\Leftrightarrow\dfrac{1}{tanx}=3tanx\)

\(\Leftrightarrow tan^2x=\dfrac{1}{3}\)

\(\Leftrightarrow\left[{}\begin{matrix}tanx=\dfrac{1}{3}\\tanx=-\dfrac{1}{3}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=arctan\dfrac{1}{3}+k\pi\\x=arctan\left(-\dfrac{1}{3}\right)+k\pi\end{matrix}\right.\)