如何把 2sin(π/12)sin(nπ/6)化成 cos(2n-1)π/12 - cos(2n+1)π/12

题目

如何把 2sin(π/12)sin(nπ/6)化成 cos(2n-1)π/12 - cos(2n+1)π/12
请尽量详细点,因为我连基本公式都几乎忘掉了,补补那些年忘记的三角函数!

答案

积化和差公式：
sinαsinβ=-1/2[cos(α+β)-cos(α-β)]
2sin(π/12)sin(nπ/6)
=cos(nπ/6-π/12)-cos(nπ/6+π/12) （提取π/12)
=cos(2n-1)π/12 - cos(2n+1)π/12