题目内容：

f(x)=(sinx+cosx)sinx-2sin(x+π/4)sin(x-π/4),若tana=2,求f(a)

优质解答

f(x)=(sinx+cosx)sinx-2sin(x+π/4)sin(x-π/4)=sin^2x+sinxcosx-(sinx+cosx)(sinx-cosx)
=sinxcosx+cos^2x =(sinxcosx+cos^2x )/(sin^2x+cos^2x)=(tanx+1）/(tan^2x+1)
f(a)=3/5