在三角形ABC中，设a+c=2b，A—C=派/3，求sinB的值。

“派”是圆周率
高一知识

根据正弦定理
a=2Rsina b=2RsinB c=2RsinC
带入
2R(sinAsinC)=4RsinB化简得
sinA+sinB=2sinB 和差化积
2sin(A+C)/2 乘 cos(A-C)/2 =2sinB
带入A-C=60°，A+C=180-B
根下3 乘 cosB/2 =2sinB/2 × cosB/2
sinB/2=四分之跟下三
cosB/2=根下（1-3/16)=根下13/4
sinB=2×（根下39）/16

解：因为a/sina=b/sinb=c/sinc=2r，a+c=2b,

故：sina+sinc=2sinb

故：2sin(a/2+c/2)cos(a/2-c/2)=2sinb=2sin(b/2)cos(b/2)

因为a-c=π/3,a/2+c/2=π/2-b/2

故：sin(π/2-b/2)cos(π/6)=sin(b/2)cos(b/2)

故：cos(b/2) cos(π/6)=sin(b/2)cos(b/2)

故： sin(b/2)= cos(π/6)=sin(π/3)

故：b/2=π/3

故：b=2π/3

故：sinb=√3/2