M=sina+cosa
N=seca+coseca
M^2/2M^2-N^2=cosa^2/2-2sina^2-coseca^2
assuming the usual carelessness with parentheses,
M^2/(2M^2-N^2)
= (sina + cosa)^2/(2(sina+cosa)^2 - (seca+csca)^2)
expand things out some, and use your double-angle formulas to simplify both sides a bit