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Prove that sin theta/1-cos theta +tan theta /1+cos theta=sec theta*cosec theta +cot theta

Prove that sin theta/1-cos theta +tan theta /1+cos theta=sec theta*cosec theta +cot theta

Grade:10

1 Answers

Rohit kumar Gupta
19 Points
5 years ago
proved tanθ1−cotθ+cotθ1−tanθ=1+tanθ+cotθExplanation:We have to prove, tanθ1−cotθ+cotθ1−tanθ=1+tanθ+cotθLet 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.

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