Question

为什么a/sina等于b+c/sinb+sinc

Answer 1

a/sinA=2R，b+c/sinB+sinC=2R(SinB+SinC)/sinB+sinC=2R，所以两式相等

Answer 2

∵ 根据正弦定理：a/sinA=b/sinB=c/sinC=2R
∴b=2RsinB，c=2RsinC
∴ (b+c)/(sinB+sinC)=(2RsinB+2RsinC)/(sinB+sinC)
= 2R(sinB+sinC) /(sinB+sinC)
= 2R = a/sinA

Answer 3

由b/sinB=c/sinC 得 sinC/sinB=c/b 两边加1得 sinC/sinB+1=c/b +1 通分得
（sinC+sinB)/sinB=(b+c)/b 变形得(b+c)/(sinB+sinC) =b/sinB
既b/sinB=c/sinC=(b+c)/(sinB+sinC)

Answer 4

a/sinA =b/sinB=c/sinC =k

a= ksinA ,b= ksinB, c=k/sinC

a/sinA = k

(b+c)/(sinB+sinC)
=k(sinB+sinC)/(sinB+sinC)
=k
=a/sinA