If sec x+ tan x
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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