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\(cosec θ=\cfrac{1}{sin⁡θ}\)

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\(tan⁡θ=\cfrac{1}{cotθ}\)
\(=\cfrac{1}{\sqrt{cot^2⁡θ}}\)
\(=\cfrac{1}{\sqrt{cosec^2 θ-1}}\)
\(=\cfrac{1}{\sqrt{\cfrac{1}{sin^2⁡θ} -1}}\)
\(=\cfrac{1}{\sqrt{\cfrac{1-sin^2 ⁡θ}{sin^2⁡θ}}}\)
\(=\cfrac{sin⁡θ}{\sqrt{1-sin^2⁡θ}}\)