(1+cos(x))/(1-cos(x))-(1-cos(x))/(1+cos(x))=4cot(x)csc(x)

= (1-cos(x)) / (1+cos(x))- (1+cos(x)) / (1-cos(x))
= (1-cos(x))^2- (1+cos(x))^2 / (1-cos^2(x))
= (1+cos^2(x)+2cos(x)-1-cos^2(x)+2cos(x))/(sin^2(x))
= 4cos(x)/sin^2(x)
=4 cos(x)/sin(x)*sin(x)
Because cos(x)/sin(x)=cot(x) and 1/sin(x)=csc(x)
= 4cot(x) csc(x)