114 嘉義女中
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Re: 114 嘉義女中
計算第 1 題
(a’^2 + c’^2 - b’^2) / (b’^2 + c’^2 - a’^2)
=2a’c’cos β / [2b’c’cos(α - β)] ，餘弦定理
= a’cos β / [b’cos(α - β)]
= sin(α - β)cos β / [sin βcos(α - β)]，正弦定理
= (1/2)[sin α + sin(α - 2 β)] / {(1/2)[sin α + sin(2 β - α)]}，積化和差
= [sin α + sin(α - 2 β)] / [sin α - sin(α - 2 β)]
= (a + b) / (a - b)，正弦定理
(a’^2 + c’^2 - b’^2) / (b’^2 + c’^2 - a’^2)
=2a’c’cos β / [2b’c’cos(α - β)] ，餘弦定理
= a’cos β / [b’cos(α - β)]
= sin(α - β)cos β / [sin βcos(α - β)]，正弦定理
= (1/2)[sin α + sin(α - 2 β)] / {(1/2)[sin α + sin(2 β - α)]}，積化和差
= [sin α + sin(α - 2 β)] / [sin α - sin(α - 2 β)]
= (a + b) / (a - b)，正弦定理