做这两道题的过程
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/24 08:38:53
8.9两道题需要详细的解题思路和解答过程。
![](http://img.wesiedu.com/upload/c/6e/c6e805c55b841dd517aa252c8b3cad07.jpg)
![](http://img.wesiedu.com/upload/c/6e/c6e805c55b841dd517aa252c8b3cad07.jpg)
解题思路: 关键是利用正弦定理进行化简即可的答案了。
解题过程:
9:b/a+a/b=6cosC:两边乘以ab
b²+a²=6abcosC
由余弦定理
c²=a²+b²-2abcosC=4abcosC
由正弦定理
c/sinC=b/sinB=a/sinA
代入上式得 sin²C=4sinAsinBcosC
tanC/tanA +tanC/tanB
=sinCcosA/sinAcosC+sinCcosB/sinBcosC
=(sinCcosAsinB+sinCcosBsinA)/sinAsinBcosC
=sinC(cosAsinB+cosBsinA)/sinAsinBcosC
=sinCsin(A+B)/sinAsinBcosC
=sin²C/sinAsinBcosC
=4sinAsinBcosC/sinAsinBcosC=4
![](http://img.wesiedu.com/upload/e/23/e23c6b0e14825506c85e1cf3af40c2aa.jpg)
解题过程:
9:b/a+a/b=6cosC:两边乘以ab
b²+a²=6abcosC
由余弦定理
c²=a²+b²-2abcosC=4abcosC
由正弦定理
c/sinC=b/sinB=a/sinA
代入上式得 sin²C=4sinAsinBcosC
tanC/tanA +tanC/tanB
=sinCcosA/sinAcosC+sinCcosB/sinBcosC
=(sinCcosAsinB+sinCcosBsinA)/sinAsinBcosC
=sinC(cosAsinB+cosBsinA)/sinAsinBcosC
=sinCsin(A+B)/sinAsinBcosC
=sin²C/sinAsinBcosC
=4sinAsinBcosC/sinAsinBcosC=4
![](http://img.wesiedu.com/upload/e/23/e23c6b0e14825506c85e1cf3af40c2aa.jpg)