高一数学

已知三角形ABC三边成等差数列，

a:b:c =sinA:sinB:sinC 2b =a+c ====>2sinB =sinA+sinC ===>2sin(A+C) =sinA+sinC sinA=sin(C+90)=cos[90-(C+90)] =cosC cosA=cos(C+90) =sin[90-(C+90)]=-sinC 2sin(A+C) =2sinAcosC+2cosAsinC =2[(cosC)^2-(sinC)^2] ===>2[(cosC)^2-(sinC)^2] =cosC +sinC 2(cosC +sinC)(cosC -sinC)=(cosC +sinC) 消去(cosC +sinC) ==>2...全部

  a:b:c =sinA:sinB:sinC 2b =a+c ====>2sinB =sinA+sinC ===>2sin(A+C) =sinA+sinC sinA=sin(C+90)=cos[90-(C+90)] =cosC cosA=cos(C+90) =sin[90-(C+90)]=-sinC 2sin(A+C) =2sinAcosC+2cosAsinC =2[(cosC)^2-(sinC)^2] ===>2[(cosC)^2-(sinC)^2] =cosC +sinC 2(cosC +sinC)(cosC -sinC)=(cosC +sinC) 消去(cosC +sinC) ==>2(cosC -sinC) =1/2 sinC =t cosC =根号(1-t^)解方程 ===>t= sinC =(根号7 -1)/4 ===>sinA =(根号7 +1)/4 sinB =(sinA+sinC)/2 =1/4 ==>a:b:c =sinA:sinB:sinC =(根号7+1):(根号7):(根号7-1) 该回答在8月9日 20:53由回答者修改过 修改回答 ┆ 采纳答案 ┆ 评论 ┆ 举报 回答：曼丽 级别：智者 8月9日 21:18 2b=a+c, 2sinB=sinA+sinC, 4sin(B/2)cos(B/2)=2sin[(A+C)/2]cos[(A-C)/2] , 4sin(B/2)cos(B/2)=2cos(B/2)cos[(A-C)/2], 2sin(B/2)=cos45°， sin(B/2)=√2/4, cos(B/2)=√[1-(√2/4)^]=√7/2√2, sinB=2×(√2/4)×(√7/2√2)=√7/4, 2C=90°-B, cos2C=sinB, 1-2(sinC)^=√7/4, sinC=(√7-1)/4, sinA=2sinB-sinC)=(√7+1)/4, ∴ a∶b∶c=)(√7+1)∶√7∶(√7-1) 。
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