The documentation on DSolve says that "NSolve deals primarily with linear and polynomial equations." You may try FindRoot if your problem is mainly numerical.

well, I have to apologise for the ill expressed question. I chopped half the equation while editing.. I have been trying to add the full equations using CodeSample with no successful so far..Would you kindly explain how I should use it?

eft

Yes, indeed some parenthesis are missing. If corrected/added (hopefully as intended in the OP it appears to work.

NSolve[(-0.38148299350912984 + 
      0.09490089588967025 Cos[x])^2 + (-0.8335932784285498 + 
      0.09490089588967025 Cos[y] Sin[x])^2 + (-0.05829052041804752 + 
      0.09490089588967025 Sin[x] Sin[y])^2 == 0.753964, {x, y}]

The solution is somewhat long and does not seem to contribute to this. Actually, I suppose that the thread will be closed because the question is only caused by a simple typo.

Anyway, here's a representation of the solutions:

ContourPlot[(-0.38148299350912984 + 
      0.09490089588967025 Cos[x])^2 + (-0.8335932784285498 + 
      0.09490089588967025 Cos[y] Sin[x])^2 + (-0.05829052041804752 + 
      0.09490089588967025 Sin[x] Sin[y])^2 == 0.753964, {x, -10, 10}, {y, -15, 15}, PlotPoints -> 50]

Cheers,

Marco

PS: Note that Mathematica suggests to use Reduce instead of NSolve. You should consider to follow that advice.