求sin3α与sinα 的关系?并求出sin18°的值（要过程）!

sin3α=sin(2α+α)=sin2αcosα+cos2αsinα
=2sinα(cosα)^2+(1-2(sinα)^2)sinα
=2sinα[1-(sinα)^2]+(1-2(sinα)^2)sinα
=2sinα-2(sinα)^3+sinα-2(sinα)^3
=3sinα-4(sinα)^3
sin（2×18°）＝cos（3×18°）
2sin18°cos18°＝4(cos18°)^3－3cos18°
∵cos18°≠0
∴2sin18°＝4(cos18°)^2－3
整理得4(sin18°)＾2＋2sin18°－1＝0
解得sin18°＝（根号5－1）/4
解法2.令x = 18°
∴cos3x = sin2x
∴4(cosx)^3 - 3cosx = 2sinxcosx
∵cosx≠ 0
∴4(cosx)^2 - 3 = 2sinx
∴4sinx2 + 2sinx - 1 = 0,
又0 ∴sinx = (√5 - 1)/4
即sin18° = (√5 - 1)/4.

sin3α=sin(2α+α)=sin2αcosα+cos2αsinα=2sinαcosαcosα+(1-2sinαsinα)sinα=2sinα(1-sinαsinα)+sinα-(sinα)^3=3sinα-4(sinα)^3顶点为36度的等腰三角形设底边是1,则腰是（1+根号5）/2（根据黄金分割...