选A.
sin²A+sin²B/sinC-cosC=√2sinAsinB
sin²A+sin²B=(sinC-cosC)*√2sinAsinB=2sinAsinBsin(C-45°)
因为sin²A+sin²B≥2sinAsinB,sin(C-45°)≤1
所以sin²A+sin²B=2sinAsinB,sin(C-45°)=1
得A=B,C-45°=90°
因为A+B+C=180°
所以A=B=22.5°,C=135°