1.
ĐK: $\sin x\ne 0\Leftrightarrow x\ne k\pi$
$\sqrt3.\cot x-3=0$
$\Leftrightarrow \cot x=\sqrt3$
$\Leftrightarrow x=\dfrac{\pi}{6}+k\pi$ (TM)
2.
$\cos2x-5\cos x+4=0$
$\Leftrightarrow 2\cos^2x-1-5\cos x+4=0$
$\Leftrightarrow 2\cos^2x-5\cos x+3=0$
$\Leftrightarrow \cos x=1,5$ (loại) hoặc $\cos x=1$
$\Leftrightarrow x=k2\pi$