证明:tanθ-cotθ/secθ-cscθ=secθ+cscθ/tanθ+cotθ

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证明:tanθ-cotθ/secθ-cscθ=secθ+cscθ/tanθ+cotθ
证明:tanθ-cotθ/secθ-cscθ=secθ+cscθ/tanθ+cotθ

证明:tanθ-cotθ/secθ-cscθ=secθ+cscθ/tanθ+cotθ
(secθ-cscθ)(secθ+cscθ)
=sec²θ-csc²θ
=1/cos²θ-1/sin²θ
=(sin²θ+cos²θ)/cos²-(sin²θ+cos²θ)/sin²
=(sinθ/cosθ)²+1 -1 -(cosθ/sinθ)²
=tan²θ-cot²θ
=(tanθ+cotθ)(tanθ-cotθ)
(tanθ-cotθ)/(secθ-cscθ)=(secθ+cscθ)/(tanθ+cotθ)