Question

Giải phương trình :\(tan\dfrac{x}{2}+1-2cot\dfrac{x}{2}=0\)

Answer 1

ĐKXĐ: \(x\ne k\pi\)

\(tan\dfrac{x}{2}+1-\dfrac{2}{tan\dfrac{x}{2}}=0\)

\(\Rightarrow tan^2\dfrac{x}{2}+tan\dfrac{x}{2}-2=0\)

\(\Rightarrow\left[{}\begin{matrix}tan\dfrac{x}{2}=1\\tan\dfrac{x}{2}=-2\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\dfrac{x}{2}=\dfrac{\pi}{4}+k\pi\\\dfrac{x}{2}=arctan\left(-2\right)+k\pi\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k2\pi\\x=2arctan\left(-2\right)+k2\pi\end{matrix}\right.\)