Answer: LHS simplifies to RHS, as shown below.
Multiply numerator and denominator of the LHS by \((\sec\theta-1)\):
\[\text{LHS}=\frac{\tan\theta(\sec\theta-1)}{\sec^2\theta-1}\]
\[=\frac{\tan\theta(\sec\theta-1)}{\tan^2\theta}=\frac{\sec\theta-1}{\tan\theta}=\text{RHS}\]