This can be simplified as follows:
1 - cos^2(α) - sin(α)cos(α) - sin^2(α)= 1 - (cos^2(α) + sin^2(α)) - sin(α)cos(α)= 1 - 1 - sin(α)cos(α)= -sin(α)cos(α)
This can be simplified as follows:
1 - cos^2(α) - sin(α)cos(α) - sin^2(α)
= 1 - (cos^2(α) + sin^2(α)) - sin(α)cos(α)
= 1 - 1 - sin(α)cos(α)
= -sin(α)cos(α)