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116问答网 > 已知cos(α+β)=12⼀13,cos(2α+β)=3⼀5,α∈(0,π⼀2),求cosα的值。

已知cos(α+β)=12⼀13,cos(2α+β)=3⼀5,α∈(0,π⼀2),求cosα的值。

已知cos(α+β)=12/13,cos(2α+β)=3/5,α∈(0,π/2),求cosα的值。

2025-03-17 00:22:14

推荐回答（1个）

回答1：

(1)cos(2α+β)=cos(α+α+β)=cosαcos(α+β)-sinαsin(α+β)=3/5
(2)sinα^2+cosα^2=1
(3)便可以解除cosα 注意sin（α+β）取两个不同的值-5/13和5/13

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