Re: [中學] 三角函數一題
※ 引述《sincetoday (sincetoday)》之銘言：
: sin20sin40sin80 =? （單位為度）
: 今天碰到這題一時想不出來，
: 謝謝！
sinθsin(60-θ)sin(60+θ)
=sinθ(sin60cosθ-cos60sinθ)(sin60cosθ+cos60sinθ)
2 2 2 2
=sinθ[(sin 60)(cos θ)-(cos 60)(sin θ)]
2 2
=sinθ[ 3/4 *(1-sin θ)-1/4 *sin θ]
2
=sinθ[(3-4sin θ)/4]
3
=(3sinθ-4sin θ)/4]
=sin3θ/4
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