在△ABC,已知tan[(A+B)/2]=sin C,求sin(C/2)的值
问题描述：
在△ABC,已知tan[(A+B)/2]=sin C,求sin(C/2)的值
请把过程列出来
答
A+B=180° -C => tan[(A+B)/2]=tan[90° -C/2]=cot C/2 =(cosC/2) /(sinC/2)
sinC=2(sinC/2)(cosC/2) =>(cosC/2) /(sinC/2)=2(sinC/2)(cosC/2)
=>cosC/2 -2(sinC/2)^2*(cosC/2)=0 =>(cosC/2)*[1- 2(sinC/2)^2]=0
=> cosC/2=0 or (sinC/2)^2=1/2
=> C/2=0不合 => sinC/2 =√2 /2 ...ans