证明 tan(π/4+α）-cot（π/4+α)=2tan2α
问题描述：
证明 tan(π/4+α）-cot（π/4+α)=2tan2α
答
tan(π/4+α）-cot（π/4+α)
=tan(π/4+α）-1/tan（π/4+α)
=[tan²(π/4+α）-1】/tan(π/4+α）
=-2/tan(π/2+2α)
=-2cot(π/2+2α)
=2tan2α