How Do You Solve: Cos(2x)/(1+sin(2x)) = (cot(x)-1) / (cot(x)+1)?

R=((cosx/sinx)-1) / ((cosx/sinx)+1)
=((cosx-sinx)/sinx) / ((cosx+sinx)/sinx)
=((cosx-sinx)/sinx) * (sinx/(cosx+sinx))
=(cosx-sinx) / (cosx+sinx)
=(cosx-sinx)(cosx+sinx) / (cosx+sinx)(cosx+sinx)
=(because^2 x - sin^2 x) / (because^2 x + sin^2 x + 2sinxcosx)
=cos2x / (1+ 2sinxcosx)
=cos2x / (1+ sin2x)
=L

by a student in WTCS