证明 cotθ – tanθ = 2 cot 2θ

题目

证明 cotθ – tanθ = 2 cot 2θ

答案

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