Question

\[ \text{If } \sec x+\tan x=\sqrt3, \]

\[ \text{then } \sec x-\tan x=\ ? \]

Solution

Using identity

\[ (\sec x+\tan x)(\sec x-\tan x)=1 \]

Substituting

\[ \sqrt3(\sec x-\tan x)=1 \]

Therefore,

\[ \sec x-\tan x=\frac1{\sqrt3} \]

Answer

\[ \boxed{\frac1{\sqrt3}} \]