Prove the trig identity: Sec^2x-Sin^2xSec^2x=1

1. Start with the left-hand side of the equation: \sec^2{x} - \sin^2{x} \sec^2{x}

2. Factor out \sec^2{x} :
\sec^2{x} (1 - \sin^2{x})

3. Use the Pythagorean identity \sin^2{x} + \cos^2{x} = 1 to replace 1 - \sin^2{x} with \cos^2{x} :
\sec^2{x} \cdot \cos^2{x}

4. Substitute \sec{x} = \frac{1}{\cos{x}} :
\left(\frac{1}{\cos^2{x}}\right) \cdot \cos^2{x}

5. Simplify:
1

Therefore, the identity is proven: \sec^2{x} - \sin^2{x} \sec^2{x} = 1