l.
ĐKXĐ: \(x\ne\dfrac{k\pi}{2}\)
\(\dfrac{1}{cotx}\left(1+cot^2x\right)=2\)
\(\Leftrightarrow1+cot^2x=2cotx\)
\(\Leftrightarrow\left(cotx-1\right)^2=0\)
\(\Leftrightarrow cotx=1\)
\(\Leftrightarrow x=\dfrac{\pi}{4}+k\pi\)
m.
ĐKXĐ: \(x\ne\dfrac{\pi}{2}+k\pi\)
\(cosx\left(\dfrac{sinx}{cosx}+2cosx\right)-2=0\)
\(\Leftrightarrow sinx+2cos^2x-2=0\)
\(\Leftrightarrow sinx+2\left(1-sin^2x\right)-2=0\)
\(\Leftrightarrow sinx-2sin^2x=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=0\\sinx=\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=\dfrac{\pi}{6}+k2\pi\\x=\dfrac{5\pi}{6}+k2\pi\end{matrix}\right.\)
n.
ĐKXĐ: \(x\ne\dfrac{\pi}{2}+k\pi\)
\(2\left(1+tan^2x\right)+3tanx-9=0\)
\(\Leftrightarrow2tan^2x+3tanx-7=0\)
\(\Leftrightarrow\left[{}\begin{matrix}tanx=\dfrac{-3+\sqrt{65}}{4}\\tanx=\dfrac{-3-\sqrt{65}}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=arctan\left(\dfrac{-3+\sqrt{65}}{4}\right)+k\pi\\x=arctan\left(\dfrac{-3-\sqrt{65}}{4}\right)+k\pi\end{matrix}\right.\)
