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51问答网 > 已知α，β是锐角，sin（α-β）=3⼀5，cos（α+β）=-5⼀13，求cos2α，cos2β

已知α，β是锐角，sin（α-β）=3⼀5，cos（α+β）=-5⼀13，求cos2α，cos2β

2025-03-25 19:22:34

推荐回答（2个）

回答1：

如图

回答2：

解由α，β是锐角，sin（α-β）=3/5，cos（α+β）=-5/13
知cos(α-β)=4/5,sin（α+β）=12/13
则cos2a=cos[(a+β)+(a-β)]=cos（α+β）cos（α-β）-sin（α+β）sin（α-β）
=4/5×(-5/13)-12/13×3/5
=-56/65
故sin2a=根(1-cos^2(2a))=33/65。

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