we know that sr = r^-1s, right? this, in turn implies sr^k = (r^-1s)r^(k-1) = (r^-1)(sr)(r^(k-2)) = r^-2sr^(k-2)

=......= r^(-k)s (the dots are the same step, applied repeatedly to move r's to the left of s).

so (r^ks)(r^ks) = r^k(sr^k)s = (r^k)(r^(-k)s)s = es^2 = s^2 = e. so that's the easy part.

now all we have to do is show that D2n = <r,s> is contained in <sr,s>; or, what is the same thing, that r and s are in <sr,s>

clearly s is in <sr,s>, and r = s(sr) is in <sr,s> as well.

(of course, we haven't shown that sr has order 2, but by the first part, sr is not in <r>, so...)