If sec x+ tan x

Given $\sec x+\tan x=\sqrt{3}$

Since $\sec ^{2} x-\tan ^{2} x=1$    (using identity)

$\Rightarrow(\sec x+\tan x)(\sec x-\tan x)=1$

$\Rightarrow \sqrt{3}(\sec x-\tan x)=1$

$\Rightarrow \sec x-\tan x=\frac{1}{\sqrt{3}}$