余弦定理是怎么证明的如题``要详细点哦``最好有式子

Question

余弦定理是怎么证明的
如题``要详细点哦``最好有式子

Answer 1

△ABC的AC=b,CB=a,AB=c,则A,B,C点的坐分别为A(b,0),B(acos C,asin C),C(0,0).
∠ACB=∠C,CB为∠ACB的终边,B为CB上一点,设B的坐标为(x,y),则sinC= =,cos C==所以B点坐标x=acosC,y=asinC.
｜AB｜2=(acosC-b)2+(asinC-0)2
=a2cos2C-2abcosC+b2-a2sin2C
=a2+b2-2abcos C,
即c2=a2+b2-2abcos C.
证明2：参考http://www.pkuschool.com/zadmin/manage/details.asp?TopicAbb=directions&FileName=g1v4sxb5570a05.htm