  We present a measurement of the anisotropic void-galaxy cross-correlation
function in the CMASS galaxy sample of the BOSS DR12 data release. We perform a
joint fit to the data for redshift space distortions (RSD) due to galaxy
peculiar velocities and anisotropies due to the Alcock-Paczynski (AP) effect,
for the first time using a velocity field reconstruction technique to remove
the complicating effects of RSD in the void centre positions themselves. Fits
to the void-galaxy function give a 1% measurement of the AP parameter
combination $D_A(z)H(z)/c = 0.4367\pm 0.0045$ at redshift $z=0.57$, where $D_A$
is the angular diameter distance and $H$ the Hubble parameter, exceeding the
precision obtainable from baryon acoustic oscillations (BAO) by a factor of
~3.5 and free of systematic errors. From voids alone we also obtain a 10%
measure of the growth rate, $f\sigma_8(z=0.57)=0.501\pm0.051$. The parameter
degeneracies are orthogonal to those obtained from galaxy clustering. Combining
void information with that from BAO and galaxy RSD in the same CMASS sample, we
measure $D_A(0.57)/r_s=9.383\pm 0.077$ (at 0.8% precision),
$H(0.57)r_s=(14.05\pm 0.14)\;10^3$ kms$^{-1}$Mpc$^{-1}$ (1%) and
$f\sigma_8=0.453\pm0.022$ (4.9%), consistent with cosmic microwave background
(CMB) measurements from Planck. These represent a factor \sim2 improvement in
precision over previous results through the inclusion of void information.
Fitting a flat cosmological constant $\Lambda$CDM model to these results in
combination with Planck CMB data, we find up to an 11% reduction in
uncertainties on $H_0$ and $\Omega_m$ compared to use of the corresponding BOSS
consensus values. Constraints on extended models with non-flat geometry and a
dark energy of state that differs from $w=-1$ show an even greater improvement.
