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Using a relatively complete observational data concerning four angulardiameter distance (ADD) measurements and %synthetic combined SN+GRBobservations representing current luminosity distance (LD) data, this paperinvestigates the %tension between compatibility of these two cosmologicaldistances considering three classes of dark energy equation of state (EoS)reconstruction. In particular, we use strongly gravitationally lensed systemsfrom various large systematic gravitational lens surveys and galaxy clusters,which yield the Hubble constant independent ratio between two angular diameterdistances $D_{ls}/D_s$ data. Our results demonstrate that, with more generalcategories of standard ruler data, ADD and LD data are compatible at $1\sigma$level. Secondly, we note that consistency between ADD and LD data %are blind ismaintained irrespective of the EoS parameterizations: there is a good matchbetween the universally explored CPL model and other formulations of cosmicequation of state. Especially for the truncated GEoS model with $\beta=-2$, theconclusions obtained with ADD and LD are almost the same. Finally, statisticalanalysis of generalized dark energy equation of state performed on four classesof ADD data provides stringent constraints on the EoS parameters $w_0$,$w_{\beta}$ and $\beta$, which suggest that dark energy was a subdominantcomponent at early times. Moreover, the GEoS parametrization with $\beta\simeq1$ seems to be a more favorable two-parameter model to characterize the cosmicequation of state, because the combined angular diameter distance data(SGL+CBF+BAO+WMAP9) provide the best-fit value $\beta=0.751^{+0.465}_{-0.480}$.

Cosmic equation of state from combined angular diameter distances: Does the tension with luminosity distances exist?