tan(x+π/4)+tan(x-π/4)化简得
问题描述：
tan(x+π/4)+tan(x-π/4)化简得
答
tan(x+π/4)+tan(x-π/4)
设a=x+π/4,则x-π/4=a-π/2
原式=tana+tan(a-π/2)
=tana-cota
=sina/cosa-cosa/sina
=-2cos2a/sin2a
=-2cot2a
=-2cot(2x+π/2)
=2cot(-2x-π/2)
=2cot(π/2-2x)
=2tan2x