Question

三角形ABC中,对边a.b.c成等差数列,且角A-C=60度,求cosB?

Answer 1

a+c=2b

正弦定理

sina/a=sinb/b=sinc/c

so

sina+sinc=2sinb

A=60+C

A+B+C=180

C=60-B/2

A=120-B/2

sina+sinc=sin(60-b/2)+sin(120-b/2)=cosbgenhao3=2sinb

tanb=genhao3/2

cosb=2/genhao7