已知向量m=(0,-1) n=(cosA,2cos^2c∕2）其中A,B,C是△ABC的内角且A,B,C依次等差数列,求|m+n|的取值范围

题目

已知向量m=(0,-1) n=(cosA,2cos^2c∕2）其中A,B,C是△ABC的内角且A,B,C依次等差数列,求|m+n|的取值范围

答案

A,B=A+d,C=A+2dA+B+C=πA+d =π/3C= A+2d= A+ 2(π/3-A)=2π/3-A|m+n|^2=(cosA)^2+(2[cos(C/2)]^2-1)^2=(cosA)^2+(cosC)^2= (cosA)^2+ [cos(2π/3-A)]^2=[cos2A+1]/2 + [cos(4π/3-2A)+1]/2=(1/2)[ cos2A - (1/2)cos...