Verify That Each Equation Is an Identity $\sec ^{2} x-1=\frac{\tan ^{2} x+\cos ^{2} x-1}{1-\cos ^{2} x}$

Verify that each equation is an identity.
- $\sec ^{2} x-1=\frac{\tan ^{2} x+\cos ^{2} x-1}{1-\cos ^{2} x}$