左边=cos²a+cos(a+b)[cos(a+b)-2cosacosb]
=cos²a+cos(a+b)(cosacosb-sinasinb-2cosacosb)
=cos²a+(cosacosb-sinasinb)(-cosacosb-sinasinb)
=cos²a+sin²asin²b-cos²acos²b
=cos²a(1-cos²b)+sin²asin²b
=cos²asin²b+sin²asin²b
=sin²b(cos²a+sin²a)
=sin²b=右边
命题得证
三角函数 cos^a+cos^(a+b)-2cosacosbcos(a+b)=sin^2b.
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