Question

利用三倍角公式,求SIN18度,COS36度的值

Answer 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^(1/2) - 1)/4

即sin18° = (5^(1/2) - 1)/4.

cos36°=1-2(sin18°）^2=((5^(1/2) + 1)/4