Question

sin^2x/sec^2x-1

Answer 1

[AI-generated answer — Explain Bot]

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.