Question

If $\sec x+\tan x=\sqrt{3},$ then sec x – tan x = ___________.

Answer 1

Given $\sec x+\tan x=\sqrt{3}$
$$\begin{gathered} \mathrm{Since}{\sec }^{2}x-{\tan }^{2}x=1\left(\mathrm{using}\mathrm{identity}\right) \\ \Rightarrow \left(\sec x+\tan x\right)\left(\sec x-\tan x\right)=1 \\ \Rightarrow \sqrt{3}\left(\sec x-\tan x\right)=1 \\ \Rightarrow \sec x-\tan x=\frac{1}{\sqrt{3}} \end{gathered}$$