Question

Simplify (sin^2⁡ x cot^2⁡x)/(1-sin^2⁡x ).

Answer 1

To simplify the given expression (sin^2x cot^2x)/(1-sin^2x), we can rewrite cot^2x as (cos^2x)/(sin^2x). After canceling out the sin^2x terms in the numerator and denominator, we get the simplified expression 1.

Step-by-step explanation:

To simplify the given expression:

(sin^2x cot^2x)/(1-sin^2x)

We can rewrite cot^2x as (cos^2x)/(sin^2x).

Substituting this into the expression, we get:

(sin^2x imes (cos^2x)/(sin^2x))/(1-sin^2x)

The sin^2x terms in the numerator and denominator will cancel out, leaving us with:

cos^2x/(1-sin^2x)

Since 1-sin^2x = cos^2x (from the Pythagorean identity), we can simplify further to:

cos^2x/cos^2x

Finally, canceling out the common factor, we get: 1