Question

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Answer 1

We have to prove, tanθ/ (1−cotθ) +cotθ /(1−tanθ) =1+tanθ+cotθ

Let us take Left Hand Side (L.H.S.) 
⇒tanθ /(1−cotθ) +cotθ/(1−tanθ)

⇒sinθcosθ /(1−cosθsinθ) +cosθsinθ1−sinθcosθ

⇒sinθcosθsinθ−cosθsinθ+cosθsinθcosθ−sinθcosθ

⇒sinθcosθ.sinθsinθ−cosθ+cosθsinθ.cosθ−(sinθ−cosθ)

⇒sin2θcosθsinθ−cosθ−cos2θsinθsinθ−cosθ

⇒sin2θcosθ−cos2θsinθsinθ−cosθ

⇒sin3θ−cos3θsinθcosθsinθ−cosθ

⇒(sinθ−cosθ)(sin2θ+sinθ.cosθ+cos2θ)sinθcosθ.1sinθ−cosθ

⇒sin2θsinθcosθ+sinθ.cosθsinθ.cosθ+cos2θsinθ.cosθ

⇒sinθcosθ+1+cosθsinθ

⇒tanθ+1+cotθ = L. H. S.

Answer 2

I hope you understand very well dear