⑩天掌 Teaching Plan on Advanced Mathematics 例1试用向量证明三角形的余弦定理 证设在△4BC中,∠BCA=BC=a,CA=b,AB=c 要证c2=a2+b2-2 ab cos6 记CB=a,CA=b,AB=c,则有 b =a-b 从而 B b c=cc=(a-b).(a-b)=a.a+bb-2a.b =la +6-2 alb cos(a, b) 由d=a,6=b,阳=c,及(Gb)=,即得 c-=a+b-2ab cos 0Tianjin Polytechnic University Teaching Plan on Advanced Mathematics 例1 试用向量证明三角形的余弦定理 记 CB a,  = CA b,  = AB c,  = 则有 c a b,    = − 从而 c c c a b a b a a b b a b              =  = ( − )( − ) =  +  − 2  2 2 cos( , ). 2 2 a b a b a b       = + − 由 a = a,  b = b,  c = c,  及 (a,b) =  ,   即得 2 cos . 2 2 2 c = a + b − ab  a  b  c  A B  C 设在 ABC 中， BCA =  ,BC = a, CA = b, AB = c, 要证 2 cos . 2 2 2 c = a + b − ab  证：