Question

Prove that : $\frac{1}{\sec x-\tan x}-\frac{1}{\cos x}=\frac{1}{\cos x}-\frac{1}{\sec x+\tan x}$

Answer 1

We have to prove that
$\frac{1}{\sec x-\tan x}+\frac{1}{\sec x-\tan x}=\frac{2}{\cos x}$
$L.H.S.=(\sec x+\tan x)+(\sec x-\tan x)$
$=2\sec x=\frac{2}{\cos x}=R.H.S.$.