The absolute value is the distance. ... If there is an absolute value of a negative number (l-6l), the distance of it away from zero cannot be a negative distance. So if the distance is always positive, then the absolute value will always be positive.
1 + sec^2(x)sin^2(x) = sec^2(x) This becomes 1+tan^2(x) = sec^2(x) which is an identity You could 1 + sin^2(x)/cos^2(x) = sec^2(x) then cos^2(x) + sin^2(x) = cos^2(x)sec^2(x) 1 = 1
