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Prove that : Sin theta /1-cos theta + cos theta/1-tan theta = cos theta +sin theta

Prove that : Sin theta /1-cos theta + cos theta/1-tan theta = cos theta +sin theta

Grade:10

1 Answers

Arun
25763 Points
4 years ago
G = (cos θ/(1 - tan θ)) + (sin θ/(1 - cot θ)) 
G = (cos θ/(1 - sin θ/cos θ)) + (sin θ/(1 - cos θ/sin θ)) 
G = (cos² θ/(cos θ - sin θ)) + (sin² θ/(sin θ - cos θ)) 
G = (cos² θ/(cos θ - sin θ)) - (sin² θ/(cos θ - sin θ)) 
G = (cos θ - sin θ)(cos θ + sin θ) /(cos θ - sin θ)
G = cos θ + sin θ 
Regards
Arun (askIITians forum expert)

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