在三角形ABC中,若4sin^2((B+C)/2)-cos2A=7/2,若

4{sin[(B+C)/2]}^2-cos2A=7/2.
(B+C)/2=π/2-A/2
4[cos(A/2)]^2-cos2A=7/2
2(1+cosA)-[2(cosA)^2-1]=7/2
2cosA-2(cosA)^2=7/2-3
(cosA)^2-cosA+1/4=0
(cosA-1/2)^2=0
cosA=1/2.
所以角A=60度.