Question:
If $\sec x+\tan x=\sqrt{3}$, then $\sec x-\tan x=$ ______________ .
Solution:
Given $\sec x+\tan x=\sqrt{3}$
Since $\sec ^{2} x-\tan ^{2} x=1$ (using identity)
$\Rightarrow(\sec x+\tan x)(\sec x-\tan x)=1$
$\Rightarrow \sqrt{3}(\sec x-\tan x)=1$
$\Rightarrow \sec x-\tan x=\frac{1}{\sqrt{3}}$
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