1.
\(cos^2x-5sin^2x-5cosx+4=0\)
\(\Leftrightarrow cos^2x+5-5sin^2x-5cosx-1=0\)
\(\Leftrightarrow6cos^2x-5cosx-1=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=1\\cosx=-\dfrac{1}{6}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\pm arccos\left(-\dfrac{1}{6}\right)+k2\pi\end{matrix}\right.\)
2.
ĐK: \(x\ne k\pi\)
\(\dfrac{\sqrt{3}}{sin^2x}=cotx+\sqrt{3}\)
\(\Leftrightarrow\sqrt{3}\left(\dfrac{1}{sin^2x}-1\right)-cotx=0\)
\(\Leftrightarrow\sqrt{3}cot^2x-cotx=0\)
\(\Leftrightarrow cotx\left(\sqrt{3}cotx-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cotx=0\\cotx=\dfrac{\sqrt{3}}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}cotx=0\\cotx=\dfrac{\sqrt{3}}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=\dfrac{\pi}{3}+k\pi\end{matrix}\right.\)
