解法1.令x = 18°
∴cos3x = sin2x
∴4(cosx)^3 - 3cosx = 2sinxcosx
∵cosx≠ 0
∴4(cosx)^2 - 3 = 2sinx
∴4sinx2 + 2sinx - 1 = 0
又0 < sinx < 1
∴sinx = (√5 - 1)/4
即sin18° = (√5 - 1)/4.
解法2. 作頂角爲36°、腰長爲1 的等腰三角形ABC， BD爲其底角B的平分線，設AD = x
則AD = BD = BC = x， DC = 1 - x.
由相似三角形得：x2 = 1 - x
∴x = (√ 5 - 1)/2
∴sin18° = x/2 = (√5 - 1)/4.
