】三角形abc 角A,B,C所对的边是a,b,c 边abc成等比数列,角A,B,C成等差数列,求sinAsinC
问题描述：
】三角形abc 角A,B,C所对的边是a,b,c 边abc成等比数列,角A,B,C成等差数列,求sinAsinC
答
2B=A+C,A+B+C=180度,推出B=60度,根据正弦定理,a/sinA=b/sinB=c/sinC=b/sin60
sinA=asinB/b,sinC=csinB/b,sinAsinC=ac(sinB)^2/b^2,而b^2=ac,故sinAsinC=(sinB)^2=3/4