  We discuss how the space of possible cosmological parameters is constrained
by the angular diameter distance function, D_A(z), as measured using the
SZ/X-ray method which combines Sunyaev-Zel'dovich (SZ) effect and X-ray
brightness data for clusters of galaxies. New X-ray satellites, and
ground-based interferometers dedicated to SZ observations, should soon lead to
D_A(z) measurements limited by systematic rather than random error. We analyze
the systematic and random error budgets to make a realistic estimate of the
accuracy achievable in the determination of (Omega_m,Lambda,h), the density
parameters of matter and cosmological constant, and the dimensionless Hubble
constant, using D_A(z) derived from the SZ/X-ray method, and the position of
the first ``Doppler'' peak in the cosmic microwave background fluctuations. We
briefly study the effect of systematic errors. We find that Omega_m, Lambda,
and w are affected, but h is not by systematic errors which grow with redshift.
With as few as 70 clusters, each providing a measurement of D_A(z) with a 7%
random and 5% systematic error, Omega_m can be constrained to +/-0.2, Lambda to
+/-0.2, and h to +/-0.11 (all at 3 sigma). We also estimate constraints for the
alternative three-parameter set (Omega_m,w,h), where w is the equation of state
parameter. The measurement of D_A(z) provides constraints complementary to
those from the number density of clusters in redshift space. A sample of 70
clusters (D_A measured with the same accuracy as before) combined with cluster
evolution results (or a known matter density), can constrain w within +/-0.45
(at 3 sigma). Studies of X-ray and SZ properties of clusters of galaxies
promise an independent and powerful test for cosmological parameters.
