1.
a,b,c成等比数列
bb=ac
正弦定理
a/sinA=b/sinB=c/sinC
2(sinB)^2=2sinAsinC=cos(A-C)-cos(A+C)=cos(A-C)+cosB<=1+cosB
2(sinB)^2<=1+cosB
0即证得02.
sinBcosB/(1+sinB+cosB)
sinB＋cosB＝t
tt－1＝2sinBcosB
2sinBcosB/2(1+sinB+cosB)
＝(tt-1)/2(1+t)
=(t-1)/2
=[sinB＋cosB-1]/2
0100<2sinBcosB/2(1+sinB+cosB)<=(√2-1)/2