f(x)=(sinx+cosx)sinx-2sin(x+π/4)sin(x-π/4),若tana=2,求f(a)
问题描述：
f(x)=(sinx+cosx)sinx-2sin(x+π/4)sin(x-π/4),若tana=2,求f(a)
答
f(x)=(sinx+cosx)sinx-2sin(x+π/4)sin(x-π/4)
=sin^2+sinxconx-(sinx+cosx)(sinx-cosx)
=sin^2+sinxconx-sinx^2+cosx^2
=(tanx+1)/cos^2
f(a)=(tana+1)/coxa^2
=3/5
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