三角形ABC中,根号3乘以sin2B=1-cos2B,求B 若BC=2 A=45° 求abc面积

1,√3sin2B=1-cos2B
2√3sinBcosB=1-(1-2sin^2B)
2√3sinBcosB=2sin^2B
√3cosB=sinB
tanB=√3 B=60
2,BC/sinA=AC/sinB,AC=BC*sinB/sinA=√6
C=180-B-A=180-60-45=75
cos30=√3/2 sin30=1/2 cos45=sin45=√2/2
sin75=sin(30+45)=sin30cos45+cos30sin45=1/2*√2/2+√3/2*√2/2=(√2+√6)/4
S(ABC)=BC*AC*sinC/2=2*√6*(√2+√6)/4/2
=(√3+3)/2