Question

在三角形ABC中,已知sinAcos^2(C/2)+sinC-cos^2(A/2)=(3/2)sinB

Answer 1

cosC=2(cosC/2)^2-1,

(cosC/2)^2=(1+cosC)/2

(cosA/2)^2=(1+cosA)/2

sin(A+C)=sinB

sin(90°-B/2)=cosB/2

sinAcos^(C/2)+sinCcos^(A/2)=3/2sinB

sinA*[(1+cosC)/2]+sinC*[(1+cosA)/2]=3/2sinB

sinA+sinC+sin(A+C)=3sinB

sinA+sinC+sin(A+C)=3sinB

sinA+sinC=2sinB