1.f（x）=cosx+sinx,
f(x+π/2) =cos(x+π/2)+sin(x+π/2)
=cosx-sinx
g(x)=f(x)*f(x+a)
=cos^2x-sin^2x
=cos2x
2.g(x)=1/2sin2x
=sinxcosx
所以设f(x)=sinx a=π/2
f(x+a)=sin(x+π/2,)=cosx
所以 g(x)=f(x)*f(x+π/2,)=sinxcosx=1/2sin2x