Question

sin(a-b)sin(b-c)-cos(a-b)cos(c-b)=???，过程

Answer 1

sin(a-b)sin(b-c)-cos(a-b)cos(c-b)
=sin(a-b)sin(b-c)-cos(a-b)cos(b-c)
=-[cos(a-b)cos(b-c)-sin(a-b)sin(b-c)]
=-cos[(a-b)+(b-c)]=-cos(a-c)
=cos(a-c)

追问

-cos(a-c)=cos(a-c)???，检查一下有没有其他的错

追答

你可以参考正弦和余弦和与差的公式
我确定没有错

追问

绝对错啦，cos(-(a-c))=cos(a-c)才对

追答

好吧

sin(a-b)sin(b-c)-cos(a-b)cos(c-b)
=sin(a-b)sin(b-c)-cos(a-b)cos(b-c)
=-[cos(a-b)cos(b-c)-sin(a-b)sin(b-c)]
=-cos[(a-b)+(b-c)]
=-cos(a-c)