为什么a/sina等于b+c/sinb+sinc
答案:4 悬赏:70 手机版
解决时间 2021-02-09 08:57
- 提问者网友：無理詩人
- 2021-02-08 15:51
为什么a/sina等于b+c/sinb+sinc
最佳答案
- 五星知识达人网友：洒脱疯子
- 2021-02-08 16:38
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
a= ksinA ,b= ksinB, c=k/sinC
a/sinA = k
(b+c)/(sinB+sinC)
=k(sinB+sinC)/(sinB+sinC)
=k
=a/sinA
全部回答
- 1楼网友：执傲
- 2021-02-08 18:50
∵ 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
∴b=2RsinB，c=2RsinC
∴ (b+c)/(sinB+sinC)=(2RsinB+2RsinC)/(sinB+sinC)
= 2R(sinB+sinC) /(sinB+sinC)
= 2R = a/sinA
- 2楼网友：我住北渡口
- 2021-02-08 18:44
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)
（sinC+sinB)/sinB=(b+c)/b 变形得(b+c)/(sinB+sinC) =b/sinB
既b/sinB=c/sinC=(b+c)/(sinB+sinC)
- 3楼网友：上分大魔王
- 2021-02-08 18:04
a/sinA=2R，b+c/sinB+sinC=2R(SinB+SinC)/sinB+sinC=2R，所以两式相等
我要举报
如以上问答信息为低俗、色情、不良、暴力、侵权、涉及违法等信息，可以点下面链接进行举报！
大家都在看
推荐资讯