cos20(tan40-根号3)=-tan40求证sin(x+y)-2cosxsiny=tan(x-y)【2cosxcosy-cos(x+y)】

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cos20(tan40-根号3)=-tan40求证sin(x+y)-2cosxsiny=tan(x-y)【2cosxcosy-cos(x+y)】cos20(tan40-根号3)=-tan40求证sin

cos20(tan40-根号3)=-tan40求证sin(x+y)-2cosxsiny=tan(x-y)【2cosxcosy-cos(x+y)】
cos20(tan40-根号3)=-tan40
求证
sin(x+y)-2cosxsiny=tan(x-y)【2cosxcosy-cos(x+y)】

cos20(tan40-根号3)=-tan40求证sin(x+y)-2cosxsiny=tan(x-y)【2cosxcosy-cos(x+y)】
第一题:
cos20(tan40-√3)=cos20(tan40-tan60)=cos20(sin40cos60-cos40sin60)/(cos40cos60)
=cos20sin(40-60)/[(cos40)/2]=-2sin20cos20/cos40=-tan40;
第二题:
等式左端=sinxcosy+cosxsiny-2cosxsiny=sinxcosy-cosxsiny=sin(x-y);
等式右端=tan(x-y)[2cosxcosy-cosxcosy+sinxsiny]=tan(x-y)cos(x-y)=sin(x-y)=左端;