定义运算:x*y=x^2-y^2+2xy则cosπ/3*sinπ/3的值是为什么(cosπ/3)^2-(sinπ/3)^2=cos2π/3?

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定义运算:x*y=x^2-y^2+2xy则cosπ/3*sinπ/3的值是为什么(cosπ/3)^2-(sinπ/3)^2=cos2π/3?

定义运算:x*y=x^2-y^2+2xy则cosπ/3*sinπ/3的值是为什么(cosπ/3)^2-(sinπ/3)^2=cos2π/3?
定义运算:x*y=x^2-y^2+2xy则cosπ/3*sinπ/3的值是
为什么(cosπ/3)^2-(sinπ/3)^2=cos2π/3?

定义运算:x*y=x^2-y^2+2xy则cosπ/3*sinπ/3的值是为什么(cosπ/3)^2-(sinπ/3)^2=cos2π/3?
cosπ/3*sinπ/3
=(cosπ/3)^2-(sinπ/3)^2+2cosπ/3sinπ/3
=cos2π/3+sin2π/3
=(3^0.5-1)/2

(cosπ/3)^2-(sinπ/3)^2=cos2π/3?这是cos2x的倍角展开式。即cos2x=(cosx)^2-(sinx)^2.