It's probably not total nonsense. There are issues arising because of the asymptotes but at least 1/sinx never gives a value BETWEEN -1 and 1 as the graph shows.

plot(1/(sinx)) - Wolfram|Alpha

Note*

is equivalent to

and in interval notation

The INTERSECTION of the 2 intervals

but the other one is OR if you interpret it as AND there is no solution.

OR

and in interval notation

The UNION of the 2 intervals.