a,
ĐK: $\cos x\ne 0$
$\to x\ne \dfrac{\pi}{2}+k\pi$
$\tan^2x+\dfrac{3}{\cos x}=9$
$\to \tan^2x+1+\dfrac{3}{\cos x}-10=0$
$\to \left(\dfrac{1}{\cos x}\right)^2+\dfrac{3}{\cos x}-10=0$
$\to \left[ \begin{array}{l}\dfrac{1}{\cos x}=2 \\ \dfrac{1}{\cos x}= -5\end{array} \right.$
$\to \left[ \begin{array}{l}\cos x=\dfrac{1}{2} \\\cos x=\dfrac{-1}{5}\end{array} \right.$
$\to \left[ \begin{array}{l}x=\pm\dfrac{\pi}{3}+k2\pi \\x=\pm\arccos\dfrac{-1}{5}+k2\pi \end{array} \right.$ (TM)
b,
PT $\to 3(2\cos^2x-1)-2\cos x-8=0$
$\to 6\cos^2x-2\cos x-11=0$
$\to \cos x=\dfrac{1\pm\sqrt{67}}{6}\notin [-1;1]$ (vô lí)
Vậy PT vô nghiệm
