函数f(x)=sin^2(x+派＼4)-sin^2(x-派＼4)是周期为?什么函数?

Question

函数f ( x ) = sin ^ 2(x + 派＼4)-sin ^ 2(x - 派＼4)是周期为?什么函数?

Answer 1

用Pi表示圆周率.
f(x)=sin^2(x+Pi/4)-sin^2(x-Pi/4)
=[sin(x+Pi/4)+sin(x-Pi/4)]*[sin(x+Pi/4)-sin(x-Pi/4)]
(利用和差化积公式)
=[2*sinx*cos(Pi/4)][2*cosx*sin(Pi/4)]
=sin(2x).
所以周期就是Pi,是奇函数.