查人人中国名人网天涯明月刀怎么摆摊:数学问题
来源：百度文库 编辑：查人人中国名人网 时间：2024/05/03 06:04:42
证明：f(x)=cos^2(x-y)-2cos(x-y)cosxcosy+cos2y+sin^2y是周期为π的偶函数（x属于R)
cos^2(x-y)
=cosx^2cosy^2+2sinxsinycosxcosy+sinx^2siny^2
2cos(x-y)cosxcosy
=2cosx^2cosy^2+2sinxsinycosxcosy
cos^2(x-y)-2cos(x-y)cosxcosy
=sinx^2siny^2-cosx^2cosy^2
f(x)=cos^2(x-y)-2cos(x-y)cosxcosy+cos2y+sin^2y
=sinx^2siny^2-cosx^2cosy^2+cosy^2+siny^2
=sinx^2siny^2+cosy^2(1-cosx^2)+siny^2
=sinx^2siny^2+cosy^2sinx^2+siny^2
=sinx^2(siny^2+cosy^2)+siny^2
=sinx^2+siny^2
f(-x)=sin(-x)^2+siny^2=sinx^2+siny^2=f(x)
f(x+Pi)=sin(x+Pi)^2+siny^2=sinx^2+siny^2=f(x)
f(x)是周期为π的偶函数