In italian calculus courses there are better proofs for limits sinx/x=1 and (cosx-1)/x=0... here the explanation is very confused, and in particular how can I say that the limits would be 1 and 0 and not, for example, 0.99 and 0.01? We use instead the theorem of comparison for the first limit (sin x < x < tan x) and a trick for the second limit (1-cos x = 2sin^2(x/2)). Very simpler and clearer.####[]