What stereochemistry results from the addition of one equiv of bromine to the #"1-methylcyclohexene"#?

#"1,2-addition"# of bromine across the cyclohexene yields the given structure:

This has 2 potential chiral centres, which are plain to see. Moreover, as written, the circumstances, the mechanism, of olefin bromination, dictate that the bromines add from opposite sides of the ring, so the bromide substituents are anti.

I cannot find a decent picture, however, this means that if the bromine at 6 o'clock project towards us, the viewer, the ipso carbon (i.e. 6 o'clock) has an #R# stereochemistry (of course, if it projects away from us it is #S#, but let's just consider the first scenario). And thus the bromine at 7 o'clock projects away from us, into the page. And thus it ALSO has an #R# geometry (check this with a model!). And so we would get 2 products #"RR"#, and #"SS"# (because 6 o'clock bromine could have conceivably pointed away from us!).

Because there is nothing to prevent the approach of the electrophile from either side of the ring, the #"R,R"# and #"S,S"# isomers should be formed in equal amounts, i.e. a racemic mix should be isolated, which would be optically inactive.

I think this is right (of course, I haven't done what I advize you to do, that is make a model and examine the chirality of each centre in 3 dimensions).

Thx to Ernest who pointed out an earlier misconception on my part.