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anhthu

$\tan x=\sqrt{3}\Rightarrow x=60^o$

$\cot x=\frac{1}{\tan x}=\frac{1}{\sqrt{3}}$

$\sin x=\sin60^o=\frac{\sqrt{3}}{2}$

$\cos x=\cos60^o=\frac{1}{2}$

$P=2\cos^2x+3\sin^2x+\cot x$

$=2.\left(\frac{1}{2}\right)^2+3.\left(\frac{\sqrt{3}}{2}\right)^2+\frac{1}{\sqrt{3}}$

$=\frac{2}{4}+\frac{9}{4}+\frac{1}{\sqrt{3}}$

$=\frac{11}{4}+\frac{1}{\sqrt{3}}$

$=\frac{33+4\sqrt{3}}{12}$.