证明 tan(π/4+α)-cot(π/4+α)=2tan2α

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证明 tan(π/4+α)-cot(π/4+α)=2tan2α

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