Lim(x->0) (tgx)^2/(1-cosx)

Lim(x->0) (tgx)^2/(1-cosx)Lim(x->0) [d((tgx)^2)/dx] / [d(1-cosx)]/dx =Lim(x->0) 2/(cos(x)^3) = 2*(Lim(x->0) 1/(cos(x)^3) = 1 / Lim(x->0) 1/(cos(x)^3) = 2/1 = 2