Question

若A+B=2π/3。则(cosA)^2+（cosb）^2的取值范围是

Answer 1

A+B=120°，B=120°-Acos�0�5A+cos�0�5B=cos�0�5A+cos�0�5(120°-A)=cos�0�5A+[-0.5cosA+√3/2sinA]�0�5=cos�0�5A+0.25cos�0�5A+0.75sin�0�5A-√3/2sinAcosA=1.25cos�0�5A+1-0.75cos�0�5A-√3/4sin2A=1+0.5cos�0�5A-√3/4sin2A=1+0.25[cos2A+1]-√3/4sin2A=1.25+0.25cos2A-√3/4sin2A=1.25-0.5sin(2A-30°)∴最大值为1.25+0.5=1.75最小值为1.25-0.5=0.75取值范围为[0.75,1.75]满意谢谢5颗星采纳！