sin^2x/sec^2x-1
To simplify the expression sin^2x/sec^2x-1, we need to rewrite the expression using trigonometric identities. Let's break it down step by step:
1. Start with the given expression: sin^2x/sec^2x-1.
2. Recall the trigonometric identity: sec^2x = 1/cos^2x.
3. Substitute sec^2x in the expression with its equivalent: 1/cos^2x.
4. Now we have sin^2x / (1/cos^2x) - 1.
5. Simplify the expression by multiplying the numerator and denominator by cos^2x to eliminate the fraction in the denominator, which results in sin^2x * cos^2x - cos^2x.
6. Factor out the common term cos^2x: cos^2x * (sin^2x - 1).
7. Recognize that sin^2x - 1 is equal to -cos^2x based on the Pythagorean identity: sin^2x + cos^2x = 1.
8. Substitute -cos^2x for sin^2x - 1 in the expression: cos^2x * (-cos^2x).
9. Simplify further: -cos^4x.
The simplified expression is -cos^4x.