证明cos²a+cos²(a+b)-2cosacosbcos(a+b)=sin²a_数学解答

证明cos²a+cos²(a+b)-2cosacosbcos(a+b)=sin²a

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解答

证明:左边=cos^2 a+cos(a+b)[cos(a+b)-2cosacosb]=cos^2 a-cos(a+b)(cosacosb+sinasinb)=cos^2 a-cos(a+b)cos(a-b)=cos^2 a-(cos2a+cos2b)/2=cos^2 a-cos^2 a+1/2-cos2b/2=(1-cos2b)/2=(1-1+2sin^2 b)/2=sin^2 b=右...