三角形ABC中,2sin^2(A+B)/2+cos2C=1,求C
问题描述：
三角形ABC中,2sin^2(A+B)/2+cos2C=1,求C
答
2sin^2(A+B)/2+cos2C=12sin^2(A+B)/2-1+cos2C=02sin^2(180°-C)/2-1+cos2C=02sin^2(90°-C/2)-1+cos2C=02cos^2(C/2)-1+cos2C=0cosC+cos2C=0cosC+2(cosC)^2-1=02(cosC)^2+cosC-1=0(cosC+1)(2cosC-1)=0cosC+1=0,2cosC-...