Question

cossq/1-tan+sinsq/1-cot =1+sin cos

Answer 1

I hope this is the question

Prove that cos A / (1 - tan A) + sin A /(1 - cot A) = sin A + cos A



Sol:
cos A / (1 - tan A) + sin A /(1 - cot A) = sin A + cos A
LHS = cos A / (1 - tan A) + sin A /(1 - cot A)
= cos A / (cos A - sin A) + sin A / (sin A - cos A)
= cos A / (cos A - sin A) - sin A / (cos A - sin A)
= (cos A - sin A) / (cos A - sin A)
= (cos A + sin A) (cos A - sin A) / (cos A - sin A)
= (cos A + sin A).
Hence proved.

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