Simone
解法1.令x = 18° ∴cos3x = sin2x ∴4(cosx)^3 - 3cosx = 2sinxcosx ∵cosx≠旁粗郑 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. 作顶角为36°、腰长为1 的运颂等腰三角形ABC, BD为其底角B的平分线，设AD = x 则AD = BD = BC = x, DC = 1 - x. 由相似三角形得：x2 = 1 - x ∴凳樱x = (√ 5 - 1)/2 ∴sin18° = x/2 = (√5 - 1)/4.
