How do you simplify Sin^2xcos^2x-cos^2x ? -Thanks

1 Answer
Jan 16, 2018

It simplifies to -cos^4xcos4x

Explanation:

sin^2xcos^2x-cos^2xsin2xcos2xcos2x

cos^2x(sin^2x - 1)cos2x(sin2x1)

We know that sin^2x + cos^2x = 1sin2x+cos2x=1, so
sin^2x -1 = -cos^2xsin2x1=cos2x
Therefore:

cos^2x(-cos^2x)cos2x(cos2x)

-cos^4xcos4x