在△ABC中角A/B/C成等差数列,求cos²A+cos²C的取值范围
问题描述:
在△ABC中角A/B/C成等差数列,求cos²A+cos²C的取值范围
答
2B=A+CA+B+C=180°3B=180°B=60°cos2A+cos2C=cos2A+cos2(120°-A)=cos2A+(-cosA/2+√3sinA/2)2=cos2A+cos2A/4-√3sinAcosA/2+3sin2A/4=5cos2A/4+3sin2A/4-√3sinAcosA/2=3/4+(cos2A+1)/4-√3sin2A/4=1+(cos2...