已知函数f(x)=2asin*x/2 *cosx/2+sin^2 x/2–cos^2 x/2(a属于R)

（1）当a=1时,
f(x)=2asin*x/2 *cosx/2+sin²x/2–cos² x/2=sinx-cosx=√2sin(x-π/4)
最小正周期为2π,
x-π/4=kπ+π/2
x=kπ+3π/4
（2）当a=2,f(x)=0时,
4sin*x/2 *cosx/2+sin²x/2–cos² x/2
=2sinx-cosx
=0
2sinx=cosx
tanx=1/2
(cos2x)/(1+sin2x)
=(cos²x-sin²x)/(1+2sinxcosx)
=(cosx+sinx)(cosx-sinx)/(sinx+cosx)²
=(cosx-sinx)/(sinx+cosx)
=(1-tanx)/(tanx+1)
=(1-1/2)/(1/2+1)
=1/3