证明 cotθ – tanθ = 2 cot 2θ

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证明 cotθ – tanθ = 2 cot 2θ

证明 cotθ – tanθ = 2 cot 2θ
证明 cotθ – tanθ = 2 cot 2θ

证明 cotθ – tanθ = 2 cot 2θ
cotθ – tanθ =cosθ/sinθ-sinθ/cosθ
=( cos^2θ-sin^2θ)/(sinθcosθ)
=cos2θ/ (1/2 sin2θ)
=2cos2θ/ (sin2θ)
=2 cot 2θ
所以原式成立

cosθ /sinθ -sinθ /cosθ =cos2θ /(sin2θ /2)=2cot(2θ )

证明:cotθ-tanθ
=cosθ/sinθ-sinθ/cosθ
=[(cosθ)^2-(sinθ)^2]/(sinθcosθ)
=2[(cosθ)^2-(sinθ)^2]/(2sinθcosθ)
=2cos2θ/sin2θ
=2cot2θ

cotθ-tanθ
=cosθ/sinθ-sinθ/cosθ
=[(cosθ)^2-(sinθ)^2]/(sinθcosθ)
=cos2θ/(1/2)sin2θ
=2cos2θ/sin2θ
=2cot2θ