ABC是三角形ABC的三个内角,且C=2B1求证sinA=3sinB-4sin的平方B2如果三角形是锐角三角形,求(AB+BC)/AC的取值范围.

Question

ABC是三角形ABC的三个内角,且C=2B
1求证sinA=3sinB-4sin的平方B
2如果三角形是锐角三角形,求(AB+BC)/AC的取值范围.

Answer 1

应该是:sinA=3sinB-4sin^3B
C=2B
sinA=sin(B+C)=sin(2B+B)=sin2BcosB+cos2BsinB
=2sinBcos^2B+(1-2sin^2B)sinB
=2sinB(1-sin^2B)+(1-2sin^2B)sinB
=2sinB-2sin^3B+sinB-2sin^3B
=3sinB-4sin^3B
即有,sinA=3sinB-4sin^3B
2)0