求复变大神,把这个化成三角函数形式
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求复变大神,把这个化成三角函数形式
![](http://img.wesiedu.com/upload/3/b4/3b4e0b4549690db7a205ff45ab1ca358.jpg)
![](http://img.wesiedu.com/upload/3/b4/3b4e0b4549690db7a205ff45ab1ca358.jpg)
![求复变大神,把这个化成三角函数形式](/uploads/image/z/18657227-11-7.jpg?t=%E6%B1%82%E5%A4%8D%E5%8F%98%E5%A4%A7%E7%A5%9E%2C%E6%8A%8A%E8%BF%99%E4%B8%AA%E5%8C%96%E6%88%90%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E5%BD%A2%E5%BC%8F)
原式 1-cos(n+1)θ-isin(n+1)θ
= --------------------------
1-cosθ-isinθ
2sin² (n+1)θ/2-2isin(n+1)θ/2cos(n+1)θ/2
=-------------------------------------------
2sin²θ/2-2isinθ/2cosθ/2
sin(n+1)θ/2[ sin(n+1)θ/2-icos(n+1)θ/2]
=-------------------------------------------
sinθ/2 [sinθ/2-icosθ/2]
sin(n+1)θ/2 [cos((n+1)θ/2-π/2)+isin((n+1)θ/2-π/2)]
=-----------------------------------------------------
sinθ/2 [cos(θ/2-π/2)+isin(θ/2-π/2)]
sin(n+1)θ/2[cos(nθ/2)+isin(nθ/2)]
=------------------------------------
sinθ/2
= --------------------------
1-cosθ-isinθ
2sin² (n+1)θ/2-2isin(n+1)θ/2cos(n+1)θ/2
=-------------------------------------------
2sin²θ/2-2isinθ/2cosθ/2
sin(n+1)θ/2[ sin(n+1)θ/2-icos(n+1)θ/2]
=-------------------------------------------
sinθ/2 [sinθ/2-icosθ/2]
sin(n+1)θ/2 [cos((n+1)θ/2-π/2)+isin((n+1)θ/2-π/2)]
=-----------------------------------------------------
sinθ/2 [cos(θ/2-π/2)+isin(θ/2-π/2)]
sin(n+1)θ/2[cos(nθ/2)+isin(nθ/2)]
=------------------------------------
sinθ/2