cos(A-B/2)=-1/9,sin(A/2-B)=2/3,且PAI/2小于A小于PAI,0小于B小于PAI/2,求c

cos[(a+b)/2]= cos[(2a-b)/2-(a-2b)/2] =cos[(2a-b)/2]cos[(a-2b)/2]+sin[(2a-b)/2]sin[(a-2b)/2]cos[a-(b/2)]=-1/9 -> sin[a-(b/2)]=4根号5/9sin[(a/2)-b]=2/3 -> cos[(a/2)-b]=根号5/3cos(（a+b）/2)=7根号5/27cos（a+b）=2cos^2（（a+b）/2）-1 =2*(7根号5/27)^2-1 =2*245/729-1 =-239/729