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

=((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