三角學問題product to sum

設 x = cos20 cos40 cos80
兩邊乘 sin20：
x sin20 = sin20 cos20 cos40 cos80
x sin20 = (1/2) sin40 cos40 cos80
x sin20 = (1/2) (1/2) sin80 cos80
x sin20 = (1/2) (1/2) (1/2) sin160
x sin20 = (1/2) (1/2) (1/2) sin20
x = 1/8

香港的課本已經很好，多看多做多檢討便會進步。若有需要，可以參考附加數學的課本

By using product to sum formula :

cos20° cos40° cos80°
= (1/2)[cos(20°+40°) + cos(20°-40°)] cos80°
= (1/2)(cos60° + cos20°) cos80°
= (1/2)(1/2 + cos20°) cos80°
= (1/4)cos80° + (1/2)cos20° cos80°

2013-04-07 22:25:00 補充：
= (1/4)cos80° + (1/2)(1/2)[cos(20°+80°) + cos(20°-80°)]
= (1/4)cos80° + (1/4)(cos100° + cos60°)
= (1/4) (cos80° + cos100° + 1/2)
= (1/4) (cos80° - cos(180°-100°) + 1/2)
= (1/4) (cos80° - cos80° + 1/2)
= (1/4)(1/2)
= 1/8

2013-04-07 22:42:18 補充：
附加數學的課本已經絕晒版...
找附加數學的pp做吧...