三角形ABC角A.B.C对边分别为a,b,c,已知A=π/4,bsin(π/4-C)-csin(π/4-B)=a⑴求角B和C ⑵若a=2√2,求三角形ABC的面积

问题描述:

三角形ABC角A.B.C对边分别为a,b,c,已知A=π/4,bsin(π/4-C)-csin(π/4-B)=a
⑴求角B和C ⑵若a=2√2,求三角形ABC的面积

(1)bsin(π/4-C)-csin(π/4-B)=a(√2/2)b(cosC-sinC)-(√2/2)c(cosB-sinB)=a(√2/2)sinB(cosC-sinC)-(√2/2)sinC(cosB-sinB)=sinA=(√2/2)sinBcosC-sinBsinC-sinCcosB+sinCsinB=1sinBcosC-sinCcosB=1...