解:(I)由题意得 , 根据正弦定理, , 两式相减,得 .……………….4分 (II)依题意,得absinC=a +b![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020065216-69630.gif) -c +2ab…………………5分 由余弦定理知:a +b -c =2abcosC……………….6分
absinC=2ab(1+cosC),即sinC=2(1+cosC)………..7分[
sin cos =2cos![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020065215-99624.gif) ……………..9分 又0 <C<180 , cos![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020065217-42805.gif) 0, sin =2cos![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020065217-42805.gif) , 即tan =2…………………………10分
tanC= = =- …………………..12分 |