Question

Simplify: sin^2xcos^2x-cos^2x

Answer 1

-cos^4(x)

Explanation:

Step 1: Use the Pythagorean identity : 1=cos^2(x) + sin^2(x)

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

-1+sin^2(x) = -cos^2(x)

cos^2(x) (-cos^2(x))

Step 2: Factor out common terms cos^2(x)

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

Ans: -cos^4(x)