  In this paper, we consider the following degenerate/singular parabolic
equation $$ u_t -(x^\alpha u_{x})_x - \frac{\mu}{x^{2-\alpha}} u =0, \qquad
x\in (0,1), \ t \in (0,T), $$ where $0\leq \alpha <1$ and $\mu\leq
(1-\alpha)^2/4$ are two real parameters.
  We prove the boundary null controllability by means of a $H^1(0,T)$ control
acting either at $x=1$ or at the point of degeneracy and singularity $x=0$.
Besides we give sharp estimates of the cost of controllability in both cases in
terms of the parameters $\alpha$ and $\mu$. The proofs are based on the
classical moment method by Fattorini and Russell and on recent results on
biorthogonal sequences.
