# Prove this equation is an identity? secx/tanx- tanx/secx=tanx/cscx

This is not an identity. The graphs of $\sec \frac{x}{\tan} x - \tan \frac{x}{\sec} x$ and $\tan \frac{x}{\csc} x$ don't lie on top of each other, therefore it is an equation and no an identity.