Answer: LHS simplifies to RHS, as shown below.
\(\sec\theta(1-\sin\theta)=\sec\theta-\sec\theta\sin\theta=\sec\theta-\tan\theta\), since \(\dfrac{\sin\theta}{\cos\theta}=\tan\theta\).
\[\text{LHS}=(\sec\theta-\tan\theta)(\sec\theta+\tan\theta)\]
\[=\sec^2\theta-\tan^2\theta=1=\text{RHS}\]
(using \(1+\tan^2\theta=\sec^2\theta\)).