1.三角形ABC中 已知lgtanB是lgtanA ,lgtanC的算术平均值,求角B的取值范围?2.已知sina+sinb+sinc=0并且cosa+cosb+cosc=0,则cos(a-b)的值是多少3.三角形ABC中,sinA+cosA=2/3,则三角形ABC的形状为?
问题描述:
1.三角形ABC中 已知lgtanB是lgtanA ,lgtanC的算术平均值,求角B的取值范围?
2.已知sina+sinb+sinc=0并且cosa+cosb+cosc=0,则cos(a-b)的值是多少
3.三角形ABC中,sinA+cosA=2/3,则三角形ABC的形状为?
答
1.lgtanB是lgtanA ,lgtanC的算术平均值 ,故:lgtanA + lgtanC = 2lgtanB = lg(tanB)^2 = lg[(tanA)·(tanC)] ,所以 ,(tanB)^2 = (tanA)(tanC) ,由于B = π - (A+B),故:-tanB = tan(A+C) = [tanA + tanC]/[1 - (ta...