A = $\frac{1}{1 - msin2a}$ + $\frac{1}{1 - msin2b}$ = $\frac{2 - msin2b-msin2a}{(1-msin2a)(1-msin2b}$
= $\frac{2-2msin(a+b)cos(a-b)}{1+m^{2}sin2asinb-msin2a-msin2b}$
= $\frac{2-2cos^{2}(a-b)}{1+\frac{1}{2}m^{2}cos2(a-b)+\frac{1}{2}m^{2}cos2(a+b)-2msin(a+b)cos(a-b)}$
= $\frac{2-2cos^{2}(a-b)}{1+\frac{1}{2}m^{2}2cos^{2}(a-b)-\frac{1}{2}m^{2}+\frac{1}{2}m^{2.}2sin^{2}(a+b)-\frac{1}{2}m^{2}-2cos^{2}(a-b)}$
= $\frac{2[1-cos^{2}(a-b)]}{[1-cos^{2}(a-b)]+m^{2}[cos^{2}(a-b)-1]}$
= $\frac{2}{1-m^{2}}$