# How do you simplify the identity: (secx-1)/(1-cosx)=secx?

Since $\sec x = \frac{1}{\cos} x$,
$\frac{\frac{1}{\cos} x - 1}{1 - \cos x} = \frac{\frac{1 - \cos x}{\cos} x}{1 - \cos x} = \frac{1}{\cos} x = \sec x$.