DiscretizeRegion fails for a triangular region

Question

Bug introduced in 10.2.0 or earlier and fixed in 11.0.0

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I define an implicit region like

R = ImplicitRegion[
  0 < Sin[u]/Cos[v] < 1 && 
   0 < Sin[v]/Cos[u] < 1, {{u, 0, 2}, {v, 0, 2}}]

But when I try to do

DiscretizeRegion[R]

Mathematica 10.4 seems to hang and doesn't return any result. This is strange, because the region is really just a simple triangle

RegionPlot[0 < Sin[u]/Cos[v] < 1 && 0 < Sin[v]/Cos[u] < 1, {u, 0, 2}, {v, 0, 2}]

and discretization of a more complex region like

DiscretizeRegion[ImplicitRegion[0 < Sinh[u]/Cosh[v] < 1 && 0 < Sinh[v]/Cosh[u] < 1, 
                 {{u, 0, 2}, {v, 0, 2}}]]

works without problems. What is the problem with my implicit triangle?

Answer 1

Looks like you've uncovered a bug. I can confirm this behavior in 10.3.1 and 10.4. You can still discretize your region using DiscretizeGraphics though:

r = DiscretizeGraphics@
     RegionPlot[0 < Sin[u]/Cos[v] < 1 && 0 < Sin[v]/Cos[u] < 1, {u, 0, 2}, {v, 0, 2}]

And if you want finer areas, use DiscretizeRegion:

DiscretizeRegion[r, MaxCellMeasure -> 0.001]