Question

here goes another sum...I have exams from Monday..pls help me. I am in class 10

Answer 1

We have to prove, tanθ1−cotθ+cotθ1−tanθ=1+tanθ+cotθ

Let us take Left Hand Side (L.H.S.) 
⇒tanθ1−cotθ+cotθ1−tanθ

⇒sinθcosθ1−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