a) $3tan2021x-\sqrt[]{3}=0$
$↔ tan2021x=\dfrac{\sqrt[]{3}}{3}$
$↔ tan2021x=tan\dfrac{\pi}{6}$
$↔ 2021x=\dfrac{\pi}{6}+k\pi$
$↔ x=\dfrac{\pi}{12126}+\dfrac{k\pi}{2021}$ $(k∈Z)$
b) $8cos^2x-4(\sqrt[]{3}+\sqrt[]{2})cosx+2\sqrt[]{6}=0$
$↔ \left[ \begin{array}{l}cosx=\dfrac{\sqrt[]{2}}{2}\\cosx=\dfrac{\sqrt[]{3}}{2}\end{array} \right.$
$↔ \left[ \begin{array}{l}cosx=cos\dfrac{\pi}{4}\\cosx=cos\dfrac{\pi}{6}\end{array} \right.$
$↔ \left[ \begin{array}{l}x=±\dfrac{\pi}{4}+k2\pi\\x=±\dfrac{\pi}{6}+m2\pi\end{array} \right.$ $(k,m∈Z)$
c) $2sin^22x-8sinxcosx+2=0$
$↔ 2sin^22x-4sin2x+2=0$
$↔ sin2x=1$
$↔ sin2x=sin\dfrac{\pi}{2}$
$↔ 2x=\dfrac{\pi}{2}+k2\pi$
$↔ x=\dfrac{\pi}{4}+k\pi$ $(k∈Z)$.
