Re: [中學] 三角恆等式證明
※ 引述《tzhau (生命中無法承受之輕)》之銘言：
: 證明tan10°=(tan20°)(tan30°)(tan40°)
: 想了好久，希望有高手幫忙，感謝。
簡便起見°就不寫了
等同證明 √3 sin10 cos20 cos40 = cos10 sin20 sin40
LHS = √3 (1/cos10)(1/8)(sin80) = √3/8
RHS = sin20 sin40 sin80
= (-1/2)sin20[cos120 - cos40]
= (-1/2)sin20[-1/2] + (1/2)sin20cos40
= (-1/2)sin20[-1/2] + (1/4)[sin60 - sin20]
= √3/8 = LHS
QED
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