化简cosψ+cos2ψ+cos3ψ+·······+cosnψ

化简cosψ+cos2ψ+cos3ψ+·······+cosnψ

要用到积化和差的公式：
式子乘以2sin(Ψ/2)再除以2sin(Ψ/2),
(cosψ+cos2ψ+cos3ψ+.+cosnψ) *2sin(Ψ/2) / [2sin(Ψ/2)]
然后将2sin(Ψ/2)移入括号里,积化和差,发现很多项都消去了,得出以下：
=[sin(3Ψ/2)-sin(Ψ/2)+sin(5Ψ/2)-sin(3Ψ/2)+…+sin((2n+1)Ψ/2)-sin((2n-1)Ψ/2)]/[2sin(Ψ/2)]
=[-sin(Ψ/2)+sin((2n+1)Ψ/2)]/[2sin(Ψ/2)]
=（-1/2+sin((2n+1)Ψ/2) / [2sin(Ψ/2)]