cos(α+β)cos(α-β)=1/3,则cos^2α+cos^2β=?cos(α+β)cos(α-β)=1/3,则cos^2α+cos^2β=?

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cos(α+β)cos(α-β)=1/3,则cos^2α+cos^2β=?cos(α+β)cos(α-β)=1/3,则cos^2α+cos^2β=?
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cos(α+β)cos(α-β)=1/3,则cos^2α+cos^2β=?cos(α+β)cos(α-β)=1/3,则cos^2α+cos^2β=?
cos(α+β)cos(α-β)=1/3,则cos^2α+cos^2β=?
cos(α+β)cos(α-β)=1/3,则cos^2α+cos^2β=?

cos(α+β)cos(α-β)=1/3,则cos^2α+cos^2β=?cos(α+β)cos(α-β)=1/3,则cos^2α+cos^2β=?
1/3=cos(α+β)cos(α-β)
=(cosαcosβ-sinαsinβ)(cosαcosβ+sinαsinβ)
=cos^2α·cos^2β-sin^2α·sin^2β
=cos^2α·cos^2β-(1-cos^2α)(1-cos^2β)
=cos^2α·cos^2β-[1-(cos^2α+cos^2β)+cos^2α·cos^2β]
=(cos^2α+cos^2β)-1
∴cos^2α+cos^2β=4/3