Question

已知三角形ABC中,sin2A=sin2B+sin2C且,2cosB*sinC=sinA,则次三角形是什么三角形

Answer 1

sinA=sin(B+C)=sin(B)*cos(C)+cos(B)*sin(C)=2cos(B)*sin(C)

so that:sin(B)cos(C)-cos(B)sin(C)=sin(B-C)=0 and that B=C

sin(-4B)=2sin(2B),and that -2sin(2B)cos(2B)=2sin(2B),so cos(2B)=-1 and B=90

so the trigle is not existed.