Prove that : tanθ/(1-cotθ) + cotθ/(1-tanθ) =1+ secθ cosecθ

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Prove tanθ/(1-cotθ)+cotθ/(1-tanθ)=1+secθcosecθ | Exercise 8.4 Q5 part(iii) Prove tanθ/(1-cotθ)+cotθ/(1-tanθ)=1+secθcosecθ | Exercise 8.4 Q5 part(iii)
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Show that: (cotθ+tanθ)/secθ=cosecθ Show that: (cotθ+tanθ)/secθ=cosecθ
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How to show that: 1+(tanθ)^2=(secθ)^2, 1+(cotθ)^2=(cosecθ)^2 and (secθ)^2+(cosecθ)^2=(cotθ+tanθ)^2 How to show that: 1+(tanθ)^2=(secθ)^2, 1+(cotθ)^2=(cosecθ)^2 and (secθ)^2+(cosecθ)^2=(cotθ+tanθ)^2