Question

在△Abc中,若lgsinA－lgsinC=lgsinB=－lg跟号2,则△Abc是何种三角形

Answer 1

lgsinA-lgsinC=lgsinB=-lg√2

sinB=1/√2

B=45 或 B=135

sinA/sinC=sinB

B=45 B=135

A+C=135 A+C=45

sinA=sinC*sinB sinA=sinCsinB

=sin(135-A)sinB =sin(45-A)cos45

=sin(A-45)cos45 sinA=sin(A-45)cos45+cos(A-45)SIN45

sinA=sin(A-45)cos45+cos(A-45)sin45 sin(A-45)+cos(A-45)=sin(45-A)

A-45=90 sin(45-A)/cos(45-A)=1/2

A=135,无解 tan(45-A)=1/2 A