(1)
cos20(tan40-√3)
=cos20(tan40-tan60)
=cos20(sin40cos60-cos40sin60)/(cos40cos60)=cos20sin(40-60)/[(cos40)/2]
=-2sin20cos20/cos40
=-tan40
(2)
左边=
sin(α+β)-2cosαsinβ
=sinαcosβ+cosαsinβ-2cosαsinβ
=sinαcosβ-cosαsinβ
=sin(α-β)
右边=
tan(α-β)[2cosαcosβ-cos(α+β)]
=tan(α-β)(2cosαcosβ-cosαcosβ+sinαsinβ)
=tan(α-β)(cosαcosβ+sinαsinβ)
=tan(α-β)cos(α-β)
=sin(α-β)
左边=右边
等式成立