函数f(x)的sin^2(x+四分子派）+cos^2(x-四分子派)-1是什么啊

f(x)=sin^2(x+四分子派）+cos^2(x-四分子派)-1
=sin^2(x+四分子派）-sin^2(x-四分子派)
=(sin(x+四分子派)+sin(x-四分子派))*(sin(x+四分子派)-sin(x-四分子派))
=(根号2*sinx)*(根号2*cosx)
=2sinxcosx
=sin(2x)
所以T=2π/2=π 奇函数

f(x) = sin^2(x + π/4）+cos^2(x - π/4) -1
= cos^2 [π/2 - (x+π/4)] + cos^2 (x-π/4) - 1
= cos^2(x - π/4) + cos^2 (x -π/4) - 1
= 2 cos^2 (x-π/4) - 1
= cos[2(x-π/4)]
= cos(2x - π/2)
= cos(π/2 - 2x)
= sin(2x)

因此是 周期为 π 的奇函数