Answer:
[tex]\large\boxed{x=\dfrac{\pi}{6}\ \vee\ x=\dfrac{5\pi}{6}\ \vee\ x=\dfrac{7\pi}{6}\ \vee\ x=\dfrac{11\pi}{6}}[/tex]
Step-by-step explanation:
[tex]12\cos^2x-9=0\qquad\text{add 9 to both sides}\\\\12\cos^2x=9\qquad\text{divide both sides by 12}\\\\\cos^2x=\dfrac{9}{12}\\\\\cos^2x=\dfrac{9:3}{12:3}\\\\\cos^2x=\dfrac{3}{4}\to\cos x=\pm\sqrt{\dfrac{3}{4}}\\\\\cos x=\pm\dfrac{\sqrt3}{2}\\\\\text{Look at the picture}\\\\x=\dfrac{\pi}{6}\ \vee\ x=\dfrac{5\pi}{6}\ \vee\ x=\dfrac{7\pi}{6}\ \vee\ x=\dfrac{11\pi}{6}[/tex]
